I have the keyless entry door, and I have already replaced the batteries in the keypad and the door motor. I have had the trailer since April, but I never use the key to lock mine.
Now as for the door sticking, I noticed that the screw heads on the latch plate were rubbing/binding on the door when it got hot or humid. The screw heads are rounded, not flat, so I took my dremel tool with a grinder bit and flattened the screw heads. I have not had a problem since. This might be something to take a look at. The dead give away will be one or two scratches above and below where the dead bolt extends out of the door.