I always try everything I can on iPads before I open them, since opening them almost always means a new screen.
Try cleaning the power button out with 99% IPA. Give it a good soaking and scrubbing. You won't hurt anything that isn't already hurt. If that doesn't fix it, its most likely just the glue on the bracket working loose after years of use. If you are pressing down on the button and it doesn't "feel right", its a safe bet that its just the bracket. It also could be that the bracket isn't lined up quite right because of a drop. It happens.