Anything is possible. Since it's a bedroom they must be large enough to provide a fire escape. (egress).

If your shed is on a cement, or there is a sidewalk leading up to the doors, it's likely that the cement under the doors is heaving due to frost (getting tight in the winter, getting loose in the summer) I've had this problem before on sheds that are not on a footing, or maybe the shed is and the sidewalk isn't and there ain't much you can do about it unless you want to make sure all the concrete is on a footing that's below frost. You could cut the doors a little more on bottom (so that they wouldn't be tight in the winter) and put an adjustable door bottom or sweep on them that you could lower as you see fit. Or attach an oak threshold to the floor that will act like a stop. (if you don't mind stepping on/over it when the doors are open) Sorry to hear about the problems. I know a house where the exact same thing is happening on a shed where I made them new doors.

Thanks for the advice. The doors have been painted, can I still apply sealer over the paint? There is an RV pad leading up to the shed and a small step made with bricks/concrete, so this is likely part of the problem. I will probably do a sweep or threshold, I hadn't thought about that. I've considered redoing the step since a few of the bricks are loose, but it sounds like I would probably just have the same problem again once it heaves.