Pat, our 2002 Ultimate Advantage had the same problem. Had an appointment to get the engine serviced a month ago; went to check the oil, etc, opened the access door and it didn't stop until it was in my hands completely off the hinges. When I investigated, it appeared that the epoxy 1) didn't adhere to the painted hinges very well, and 2) didn't hold in the holes that it was spread into. It probably would still be on if there was more epoxy 'through' the hinge, instead of just 'on' the hinge.
I had noticed the attachment process earlier and never did really like it, thinking this exact thing would happen. I think over time, heat actually is the culprit.
So this time, I used an automotive grade epoxy (GOOP) and 6 #8 stainless steel bolts, nuts, and lock washers. It was a little tricky getting those into the hinge plates, but I pushed the bolts through from behind the plates and then glued them to hold them snug until I could put the access door on with the nuts and lock washers. I topped the bolts off with cap nuts.
I probably would have had the same issue on the front of the coach, but 2 years ago, I hit a 2x2x3 box full of christmas toys doing 70mph in Georgia. Luckily, it only destroyed the fiberglass panel attached to the generator rollout frame. Didn't do hardly any damage to the front or the cap. The resulting repair fixed the potential for that door to fall off.
Be careful in Georgia at xmas time....lots of pickup truck santas delivering presents.