B-737-800 Captain reported a hydraulic malfunction during cruise flight. The flight continued to the destination and landed but the main gear tires failed during the landing and the aircraft required a tire change on the runway.

Narrative

The factors leading to this event were numerous and will be outlined in sequential order. On flight ABCD from ZZZ1 to ZZZ. With an initial departure time of XA:46; the inbound aircraft arrived late to ZZZ1 from ZZZ2 at XB:51 which was approximately 2hrs 5mins behind schedule due to thunderstorms in location X; holding and ground delays that were experienced upon this crew's arrival. Once our aircraft arrived at our gate in ZZZ1; the aircraft also had 8 open write ups (numerous power outlets; three passenger seat reclines; sidewall lighting; and FA jumpseat lighting) that needed tending to before we would have been able to board. Prior to the crew and I stepping onto the aircraft; a call was made to our dispatcher informing him of a maintenance delay and the dispatcher and I (the captain) would be delaying boarding for the maintenance technicians to work on the aircraft in the main cabin as well as a delay for boarding due to extended ground delays for all departing aircraft in ZZZ1 ranging from 2.5 - 3hrs. This was communicated to our gate agents as well. While our maintenance personnel worked to fix our cabin write ups; the First Officer and I (CA) began setting up the flight deck so that we could depart in a timely manner once we were given the opportunity to board and get our passengers on board. It was at this time that the First Officer and I would discover that we were having issues with the aircraft's ACARs system when we were prompted with a Datalink" and "Voice Only" message on the FMS. A new write-up was entered into the Logbook and maintenance would later arrive to work on resolving the issue. Frequent conversations were had with our dispatcher to receive updates on the ground delays in ZZZ1 as well as for me to give him updates on the status of our maintenance situation. The ACARs writeup ultimately concluded with the system being deferred as "INOP" due to the majority of it's functions being inaccessible (ATIS retrieval; takeoff data; CPDLC; PDC; OOOI times etc.). Once the maintenance team concluded their work in the cabin and Maintenance concluded their work on our ACARs situation; a status update was given to our dispatcher; and it was at this time; the dispatcher analyzed ZZZ1's departure delays and gave us the green light to board the passengers and prepare for departure. These updates were continuously forwarded to our gate agents; and we began to board. After pushing off the gate; at XE:25 we found ourselves number 29 in line for departure. Unsure of how long it'd take for us to depart wheels up; the tarmac delay application was used to ensure that we remained in compliance with the FAA DOT extended ground delay regulations. Due to our ACARs deferral; the dispatcher update component of this extended ground delay component was accomplished via voice phone calls from my cellular device. We were finally able to get airborne for ZZZ. About 60 minutes into our flight; our flight attendants called the flight deck notifying us that a passenger in the main cabin was experiencing nausea symptoms that the portable oxygen was now in use. We informed them to keep us updated with the status of the passengers' health; I reduced the main cabin's air temperature to a colder setting for the passenger. After our call with the flight attendants were made; I ensured that the FO continued his PF duties as I referenced the Medical Emergency Flow Chart located in the FOM preparing for all contingencies. Roughly 20 minutes later; we received an update from the flight attendants regarding the passenger's health; and it was reported that they were in a stable condition. We continued the flight as planned and a Logbook entry for the POB (Portable Oxygen Bottle) would later be accomplished. 40-60 minutes later the FO and I would receive a master caution light for an ENG 1 Low Pressure. The FO (PF) stated; "My Aircraft" we acknowledged the annunciator; the FO continued his PF duties as I (CA) referenced the QRH for the associated issue. The QRH instructed us to turn off the ENG 1 pump and that the associated electrical pump (ELEC 2) would pick up system A's load. As this is being accomplished; the FO and I are referencing the hydraulic system's synopsis page where we discover that we had a continuous decrease of system A hydraulic quantity %; though we were maintaining positive hydraulic pressure of 2940-3000 psi. Shortly after this verification; system A hydraulic quantity would drop below 10%. After ensuring the FO remained facilitating his PF duties; he was also given control of the radio's as well. Though the Low Pressure QRH procedure did not conclude in a recommendation to divert or "land at nearest suitable airport" I made the decision to patch in dispatch and maintenance control to bring them in the loop and discuss contingencies. Because our ACARs system was INOP; contacting dispatch by these means was not possible so I attempted to contact our dispatcher via app. After multiple attempts; the call continued to fail; and we were unable to contact our dispatcher via this method. I would bring my attention back into the flight deck to check in with the FO to ensure that he was not overloaded and that no significant changes were made or experienced while I was attempting to use the app and the FO confirmed that everything was stable and under control. Once this was acknowledged; I brought my attention back to contacting dispatch. We were flying over location Y; so I elected to contact dispatch via Dispatch Direct VHF Network with the appropriate frequency found in our FOM. Contact with our dispatch established and I was able to inform our dispatch and maintenance control of the situation. Maintenance control confirmed with us that system A was maintaining positive system hydraulic pressure and advised us to continue the flight as planned; the dispatcher concurred with this as well. Once the call was concluded; I advised the FO of the plan; and we were all in agreement that this flight could be continued safely and that we would always keep our hydraulic system synopsis page in view to monitor its pressure. Roughly 60 minutes later; we would experience another master caution light; this time for ENG 2 Low Pressure. The FO (PF) stated; "My Aircraft"; acknowledged the annunciator and repeated the sequence of steps that we did for ENG 1 Low Pressure for now ENG 2 Low Pressure. The FO continued to fly the aircraft; and I (CA) referenced the QRH for ENG 2 Low Pressure. As before with ENG 1; the QRH instructed us to turn off the ENG 2 pump and that it's associated electrical pump (ELEC 1) would pick up system B's hydraulic demand. Monitoring the system B pressure on our hydraulic synopsis page; we confirmed that the aircraft maintained positive hydraulic pressure and quantity. Respecting the QRH procedure as we did for ENG 1; the Low Pressure QRH procedure did not conclude in a "land at nearest suitable" and recalling the prior conversation that was had with dispatch and maintenance control; we knew that if we were able to maintain positive system pressure; continuing as planned to our destination was the best bet.Once the QRH procedure was concluded for ENG 2 Low Pressure; the FO and I checked in with each other making sure we were both able to continue. Once this was confirmed and though our hydraulic system indicated that we were maintaining positive hydraulic pressure on both systems; I brought my attention back to the QRH to proactively read the "Loss of System A;" "Loss of System B" and "Loss of System A and Loss of System B" QRH procedures in case our situation worsened. It was determined that if we experienced a "Loss of System A and Loss of System B" with our current weight and weather conditions; 7985 ft. was required for our landing distance and that we could request priority handling and divert to our nearest suitable airport which would be ZZZ3 - listed as an adequate alternate airport with runway XX having a LDA (Landing Distance Available) of 8;118ft. With having our worst-case contingency plan agreed upon; and after ensuring that the FO was still fulfilling his PF duties; I shift my focus to the most probable emergency we could experience which was reviewing the QRH procedure for "Loss of System A." I deemed this "most probable" because while system A's hydraulic pressure remained between 2940 3000 psi; it's quantity % continuously fluctuated between 0-10% whereas system B quantity % and pressure remained constantly stable within the AOM's limitations. Reviewing the "Loss of System A" QRH procedure; our biggest concern was ensuring that our landing gear would probably extend and in the event that we would have to accomplish this procedure; that the FO and I gave ourselves enough time to facilitate this lengthy QRH procedure which involves manually extending the landing gear. At this point we are just shy of 60 minutes from our arrival to ZZZ and that considering ZZZ4 as an airport to divert to did not seem to be the best course of action as that airport was experiencing IROP's (Irregular Operations) due to storms; lengthy ground delays and minimal gate availability. Our planned arrival runway at ZZZ was XXR. With 12;250ft of LDA; winds directly out of the south at 5kts and VFR conditions; continuing to our planned destination was the safest option as the land app only required a landing distance of 5;195ft based off dry conditions and 6;729ft for wet conditions. Once our decision to continue to ZZZ was made; we further concluded that we would have ATC vector us onto the final approach course just outside of the ZZZZZ intersection on the ILS XXR approach; to give us a 15nm final to ensure that we get into landing configuration and stable as early as possible with our gear down. Once this plan was formulated and agreed upon with both the FO and I (CA); we began preparing for our arrival by accomplishing all the required normal briefs; verifications and checklists associated with the descent and arrival phase of flight. As we approached the terminal environment for ZZZ airport; 23nm to the north inbound for the ILS XXR; slowed to 179kts and flaps 5; we extended the landing gear before selecting flaps 15. Once the landing gear handle was set to the down position; a 4 second delay was experienced before we felt the landing gear deploy. We determined that this was a probable result of electrical hydraulic pump using the remaining 20% of fluid in system A to actuate the landing gear. After verifying that we had a 3 green indication on both the primary landing gear indicator as well as the landing gear position indicator on the aft overhead panel; we continued to configure for our approach; ultimately being fully configured for landing 10nm's out just prior to the ZZZZZ intersection. Approaching 1;000ft and stable for the ILS XXR; we received a master caution for an intermittently flashing low pressure light on the ELEC 2 hydraulic pump. The FO states; "My Aircraft"; we acknowledge the master caution light and quickly notice around 900-800ft that we are beginning to experience a total loss of system A hydraulic pressure as the hydraulic pressure begins to decline rapidly. As the Captain; multiple decisions and considerations were made at this moment. Option 1: Execute a go-around with the inability to retract the landing gear; request priority handling; fully run the "Loss of System A" QRH in holding operating on only one hydraulic pump (ELEC 2); risk experiencing a loss system B which would then lead us to running the QRH procedure for "Loss of System A and Loss of System B"; with a rapidly increased workload or; Option 2: Use Captain's Authority as outlined in the FOM; request priority handling and continue the approach as is. Considering we were approaching 500-600ft; fully stable with a confirmed landing gear in the down position; already concluded that we have the required runway distance available for the Loss of System A and not willing to entertain the idea o"