Here’s a tip that I found handy recently, and perhaps you may too. On my iPhone 4, it seemed that the home key (the big button at the bottom of the iPhone that exits apps) was getting hard to press. It would take several hits to make the button register, and when using it to check the time on the device it was taking even more tries.
But there is a simple solution to this problem. Turn on the iPhone, and hold the top right power button (on the top edge of the device) until you see the “slide to power off” screen. At that point press and hold the home key (round button with square emblem at the bottom of the screen) until the regular screen returns. At this point, the physical home key is re-calibrated, and it should work much better.
It might be good to note that you don’t want to mash the home key really hard when calibrating it, or it will take a really hard mash to make it work. Instead, use regular pressure, and hold steady until the screen returns. This is a simple solution that could be easily overlooked if your home button is starting to be less responsive.
But if your Home button simply refuses to respond to calibration, consider using the Assistive On-Screen alternative as a workaround.