A321 Captain reported all navigational information on both MCDUs was lost during departure climb. Flight continued to destination and landed.

Narrative

I was the Captain on flight ABCD from ZZZ-ZZZ1. We were on an 321 aircraft with XXX souls on board and 2 pilot jumpseaters. Shortly after departure and passing through 10K feet; I reached down to select a wind update and noticed there was no selectable prompt. I then noticed there was an 'ACARS Standby' message on the ECAM. Passing through approximately 11K; accelerating to 320 kts and heading westbound on the ZZZZZ departure; we lost all navigational information from both our MCDUs (Multipurpose Control Display Unit) including our courses; waypoints; performance data; and our departure and arrival stations. The aircraft went into heading mode; continued its climb as previously directed and went into selected speed but was slowing automatically to 250 kts. We selected 300kts and continued to climb on our current heading. We also received a 'CABIN PR Landing Altitude' ECAM warning. The FO was PF and I directed him to continue flying while I tried to reinsert the plan. There were no prompts to reinsert into the primary flight plan; so I reloaded the flight plan into the secondary flight plan. Initially; the aircraft accepted the reinserted information in the secondary FP and began navigating off of it as normal. This lasted for approximately 2 minutes; then both MCDUs dropped all information once again. Each time the flight plan dropped; we received the ECAM Cabin PR warning I mentioned earlier. The aircraft returned to the parameters I previously mentioned. At this point; I directed the FO to go to MAN pressurization and monitor it. I also asked the pilot jumpseaters to help the FO manage the pressurization so the masks would not drop since I was busy talking with dispatch and Maintenance Control. I then radioed ATC we were having navigational issues and requested radar vectors towards our planned course until we can figure out our issues. ATC acknowledged and graciously provided vectors and climb altitudes. We tried to reinsert the flight plan into the #1 and #2 MCDUs no less that 15 times and also tried to swap the aircraft's database the same amount of times with no success. We would occasionally be able to reload the plan into the secondary flight; but never was able to reinsert back into the primary flight plan. When the secondary flight plan would be accepted; the aircraft would go back into its NAV function; but again this lasted no more that 2 minutes before it subsequently dropped all data once more. From approximately 11K feet until the ZZZ VOR near ZZZ2; we flying on vectors from ATC with selected speed. Utilizing the assistance of our dispatcher and Maintenance Control; we could not identify any particular faults; nor any computer resets that matched the issues we were having. After all agreeing the best course of action would be to continue to ZZZ1; I expressed my concern of whether the aircraft would give me any landing performance information since both MCDUs were not displaying any of our flight plan information. No answer was able to be given to my question and we agreed for me to call back abeam ZZZ3 to discuss again. While I was talking with dispatch and Maintenance Control in the vicinity of the ZZZ VOR; the FO reinserted the plan into the secondary flight plan on MCDU2; after swapping the aircraft's database database once again; and the aircraft started to NAV again. This time; the information held. I informed ATC it appeared we were able to navigate on our own again and they cleared us into ZZZ1. We took this time to brief the approach early since we anticipated many threats. I informed the FO that I intended to take the landing and told him I planned to disconnect the autopilot and auto thrust for landing as we did not know how the aircraft would behave without performance data if the flight plan dropped on the approach. We discussed that I planned to hard tune the ZZZ1 [localizer] frequency for the approach; and that if we have our flight plan drop out again on the descent/arrival; I intended to notify ATC for our navigational issues since I would not be able to comply with the lateral or vertical requirements of the ZZZZZ1 arrival. We took note of the predicted landing performance calculations; wrote them down and I informed the FO I would use selected speed just in case the information dropped out for the approach. About this time; we were approaching ZZZ3 and I again called dispatch and Maintenance Control. I informed them of our arrival plans to include manually flying the airplane in; and they concurred. Maintenance Control advised me to write up the issues as '#1 FMGC would not hold the flight plan longer than 2 minutes after takeoff'. I then assumed PF and we began our managed descent on the ZZZZZ1 arrival from 30K feet as normal. Somewhere between the ZZZZZ2 and ZZZZZ3 fixes; the flight plan dropped again. The aircraft went into vertical speed and selected speed. I directed to FO notify ATC to navigational issues and request radar vectors and step down altitudes for the ILS to runway XXL. ATC immediately agreed and began providing those services. ATC asked were we were requesting priority handing; we told them no; just requesting no delay. About 3 minutes later; ATC informed us due to 'management preferences' they were going to give us priority handling and have the ARFF vehicles standing by. We acknowledged this information. As briefed; I disconnected the autopilot and auto thrust and landed the aircraft with selected speed on runway XXL. We exited the runway as normal and taxied to gate XX.