The iPad home button is only affixed to the screen by double-sided adhesive tape on each side of the home button bracket. It is very probable that just wear and tear has degraded the adhesive tape, and it is beginning to let go on the top edge of the bracket mounting pads.
When i replace a screen, I will remove the adhesive tape on the home button bracket, clean the surface the bracket mounts to with isopropyl alcohol, and then reinstall the button using B7000, as this will be far more secure than double-sided PSA tape.
Unfortunately, there is no way to rectify this without opening the iPad. Opening and properly re-sealing an iPad, is not a job for the faint of heart, so if you don’t know what you’re doing, take it to a reputable repair shop.