There are a range of possible fixes. Have you tried the following?
Recalibrating the home button appears to fix the issue for a majority of the users. It happened with our iPhones here. When the home button gets a bit tricky and unresponsive, this is what we usually do:
- Open an app. Any default iOS app. (Weather, Clock etc.)
- Hold the Sleep/Wake button (Power) till the ‘Slide to power off’ appears
- Now press and hold the home button till the slide goes away and you get to the homescreen.
(You’ll notice that the app is closed)
This should fix the calibration issues and make the home button work better. Of course, while the thing works well, the calibration appears to wane away after sometime. For some, this happens within a week or so. For some, this happens after several weeks or months.
Cleaning / Dusting
Sweat causes moisture. There’s dust all around. And with the kind of little spaces that the home button’s edge has, it is very much possible that the unresponsiveness is due to dust clogged in it. Usually, repair takes up a lot of time and money so you can try cleaning the thing yourself.
One of the best ways to clean the home button without having to play around with the screws is to just press the button and air dust it. This usually blows away some of the clog dust and helps you get back some good responsiveness with the home button.
If all else fails:
Reset: go to Settings -> General -> Reset -> Reset All Settings. Have a data backup just in case.