I think its a matter of the heat from the fire is hottest at the center of the door, and all around the edges is a little cooler. Since the cooler metal is not expanding as much as the hot center, that center still needs some place to push out, so eventually it bends to give it somewhere to go. The sides of the stove don't bend because they're not held on by a hinge only on one side, they're welded down to their neighbor all the way around. If you run the stove enough, you may eventually notice that the middle of the panels will start to show a bow or sag in spots, especially if it gets up to a dull red there when you're running it.
A bunch of the stoves I've seen have cast iron doors, which I suspect don't bend and warp as much as the red iron.
I've seen some stove doors that are actually double, both to act as a baffle to direct the air from the air controls down low to the fire, and so that the inner layer acts as a heat shield so the outer layer doesn't see as much heat.
Do you think you can straighten out your existing door again, maybe in a press? How about adding a sheet of heavy stainless (16 ga or so, maybe) to the inside surface with maybe a 1/2" to 1" gap using bolts or some similar kind of stand off. If that sheet then decides to bend, or even bend enough to bend the mounting bolts/posts then it still shouldn't be noticable on the outside or affect the seal. You'll lose a little length in your firebox (and I know that can be an issue if all your wood is cut to just fit what it is now). When it gets too mangled (more than likely from trying to slam the door on a slightly too long piece of wood) just replace it and keep going. Stainless bolts would have a better chance of coming apart again later for these repairs (it works on mufflers up here in the land of winter salt, anyway).