Could software cause the iPhone's home button to become unresponsive?
Do you close your open applications often? If you tap twice on your home button so the last used apps bar on the bottom comes up there if you hold any of those icons for about 2 seconds pushed in, where after they will start to jiggle and you'll see an red close icon on the top left of those recently opend apps icons will show. Tap that! and the app will close and make space in memory. If opening up memory by hand doesn't work I'd suggest you check the connection of the button.