B737-800 flight crew performed a rejected takeoff due to Aft Entry warning light.

Narrative

The rejected takeoff was on Runway XX; RWY length 1X;XXX ft; Planned for a Flaps 1 bleed on; 22K Dry; N1 89.7; V1/146; V2/147; VR/150; AT (Auto Throttle)/42C. TOW (Take-off Weight)/144.1. XXX SOB (Souls on Board). We were cleared for Takeoff and Power was set to 89.7. First Officers Takeoff. At approximately 110 knots Master Caution light illuminated as Pilot Monitoring I looked up and saw AFT ENTRY warning light illuminated; I stated 'Reject my aircraft' Pulled the throttles to idle simultaneously disconnecting auto throttles; confirmed Speed Brakes deployed; full reverse thrust; and RTO (Rejected Take-Off) brakes applied. The reject was successful all procedures followed and ATC Transmissions made per SOP. We cleared the runway at Taxiway 1 approximately halfway down the runway. No injuries and no aircraft damage. Outside air temp was +28; brake on at approximately 110kt; GW (Gross Weigh) 144.1. Once clear of runway and stopped; made a PA to passengers and informed them of why we stopped; reassured them all is OK and remain in their seats with seatbelts fastened and that we had to return to the gate. At the apron Spot X; we shut down the aircraft and were met by airport personnel; Maintenance and we completed a walk around to check on brake temperatures and cooling times. ARFF (Airport Rescue and Firefighting) was nearby even though they were not requested but in hindsight probably should have requested them after the reject just in case the brakes heated up. We did check the brake cooling chart and concluded that the threat of thermal plugs; brake temperatures did not require ARFF supervision; however out of caution I the Captain should have requested them just in case. I made an AML (Aircraft Maintenance Logbook) entry in logbook stating reason for reject; speed brakes applied approximately 110kts; GW144.1 and outside temp of +28. Along with Master Caution and AFT ENTRY illumination. As the Captain; I made my decision to reject based on numerous factors. First; I knew we had over 1X;000ft of runway and that stopping on the runway would not be a factor; Second; considered aircraft not fit for flight because it was an aft entry door and not knowing if the door opened or not played a role in my decision. Since the aft door is located near the tail and critical flight controls did not want to get airborne and complicate the event. Therefore; used Captain Authority to make the decision to reject. As event was occurring; I did consider the threat of hot brakes and continuously and immediately checked to see if it would play a factor once the aircraft was safely stopped and all procedures were followed. First Officer ran the brake chart and it was determined that hot brakes were not an immediate fire hazard and that we required approximately 40 min of cooling time. After the event was over and back in the chocks; engines shutdown; Maintenance doing their inspection; 1 of the passengers that did have a heart condition was not feeling well; so ground personnel removed him from flight and took control of him. No immediate life-threatening conditions were noted other then he felt weak and light headed and requested to be taken off the flight. Which we complied with. I was also met with a ZZZZ aviation safety person who did not speak very good English that requested a handwritten account of the event; which I complied with and signed but was not presented with a copy of the form. With all of the logistical issues of Maintenance; passenger control and company inquiries things were very busy. To compound the issue it was our 3rd leg that day of a 4day trip and we were facing timing out for duty day. It was the last leg of the trip and we didn't have much time left. Since; we do not routinely remain overnight in ZZZZ and considering the passengers limited options for successfully getting to ZZZ; we the pilots agreed to extend our duty day by 2hr and tried to complete the flight. After a lengthy delay; we were able to get the aircraftsigned off by Maintenance and continue the flight to ZZZ. Cause: Pilot fatigue definitely played a role in this; but thankfully it all ended well. To mitigate risk; crew pairings should not be scheduled routinely right up to the maximum allowed by the FAR's. It does not allow any room for error and ultimately results in reducing time for crew to get adequate meals; rest between flights and during overnights. When delays happen for anything; company routinely reduces the time between flights and takes the delays out of crew down time between flights and during overnights further compounding the fatigue issue. This builds up over a 3;4;5 day trip and you end up with a fatigued crew pushing limits thy should never have to do. It is not a safe practice; but a practice that optimizes the company's utilization of every possible minute a flight crew is a legally available. It's not safe and really needs to be stopped before something critical happens. Our only recourse is to call fatigued; but if you do it routinely you could be putting your career on the line. Not a mindset an aircrew should be faced with when determining FIT FOR DUTY. FAR duty limits are just that. Limits. They should not be allowed to routinely schedule trips to fly continuously right up to those limits. When you complete trips they way they are scheduled now crew members are completely exhausted approaching the last day of a trip because of compounding factors over a 3;4;5 day sequence that results in a fairly fatigued crew rejecting at high speed on the last leg of a 4 day trip. Also the time during overnights are based on block in to block out times. Example: Land at XA:00 and next leg departure is scheduled for a XM:00 takeoff; therefore your time during overnight is 12hrs. Sounds reasonable; however factor in that it takes on average 1hr to get from setting brakes to get to the hotel and now you are down to 11hr rest; then factor in another 30 min to check in; get changed and think about getting something to eat; now you have 10.5hr rest; then assuming you can find somewhere to get something to eat; factor 1hr to sit and try and enjoy a meal now you are at 9.5hr; then plan on a van time that will get you to sign in 1hr prior to flight; so backup your wake up time to allow for shower; and packing up to be in lobby by van time and at a minimum that 2.5hr prior to departure so you are now down to 7hr of sleep. Assuming you can immediately fall asleep based on the timeline which never happens. This leaves crews getting an average of about 5-6hr of sleep at night assuming no hotel interruptions. Now do the same over 3 days and note that each day may have 2 to 3 legs which throughout the trip have issues with delays that eats away at crew members times to get food in between flights or just stretch their legs. Bottom line; the schedules are becoming more and more demanding with the companies trying to squeeze every legal minute out of a crew member to so call 'Optimize' the schedule and increase profits and it is becoming a very dangerous; unhealthy practice that is leading to more fatigue calls and overall unhealthy lifestyle for a profession that requires the highest medical standards. This in my opinion will someday lead to a fatigued crew member pushing the limits because of fear for calling fatigued too many times; financially loss or just trying to take care of the passengers and will lead to an aircraft accident. It is becoming more and more common place to schedule and push these limits. I hope that someone will look into the FAR Duty Day and flight day limits and set new guidelines that track crew rest times with clear start and end points. Example. My 12hr overnight rest should be started based on the avg time it takes to arrive at the hotel and should run to sign in. Not block to block. Examine this practice further and you will see more and more crew members are experiencing the same issues and fatigued pilots are becoming the normal. Last thing anyone wants is a malnourished; fatigued pilot making critical decisions at key times like a rejected takeoff. I hope something changes.