The problem could occur because of two reasons –
1. The software may be faulty.
2. The hardware might be faulty.
If it is the latter, you will need to go to Apple and get a new iPhone. If the problem is with the software, one needs to try out the following methods.
A problem with the software usually is set right when you do a restoration of the iPhone OS. You can either do a restore from the backup, or do a complete restore if you don't have much data to worry about. Restoring from the backup or from scratch lets you reconfigure all your software settings so that whatever it is that was bugging the home button on the iPhone would go away.
However, some people have reported that both the types of restore does not bring the intended results. Here’s one more method which seems to work in favour of some iPhones. You could try it too.
Open any application on the iPhone
Press and hold the Power button till the ‘Slide to Shutdown’ screen appears.
Now release the Power button and gently hold the Home button.
In all probability, your Home button would start functioning normally again!
You can also try deleting all your shortcuts, by double tapping the home button, and deleting the App's that appear in a single horizontal line at the bottom of the screen.
In the case that it fails to do so even after all this, you’ll definitely need to check out the hardware part. If you have just recently bought the device, then you get a replacement warranty so you can make use of that to get a new device quickly.
Edited by Apparelyzed, 09 February 2012 - 03:05 PM.