This is clearly a hardware issue, and am pretty sure that if i send it in under warrantee, water will be blamed, this even happens if you live in a dessert and are close to death due to dehydration.
Go into Settings, Accessibilty, AssistiveTouch, switch "On", now use the on-screen Home button. I've gotton so used to the on-screen Home button, I hardly use the physical button anymore, and there is no more "wear and tear" on the physical button. Hope this tip is useful to any of you.
Once re-calibrating doesn't work I've used surgical spirits on the home button a few times and on a few iPhones.
I turn the phone off. Soak a cloth in surgical spirits and rub the button vigorously. For the next few months it works great.