if you're out of warranty, the repair is possible but only with a fee.
If you go to a retailstore, you'll need an appointment at the genius bar. But before you can be sure there's a repair needed, try this:
1. Try doing a hard reset:
Press and hold both the Home button and the Sleep/wake button simultaneously for about 15 seconds and release when the Apple logo appears.
2. If that doesn't solve the issue, backup the device and restore it as new.
In that case, use: http://support.apple.com/kb/HT4137
NB: set up as a NEW device because a software issue will be in the backup. If the issue persists after restoring as new, you should offer the device for service.
If you get specific error messages/codes in iTunes when updating/restoring, check this: http://support.apple.com/kb/ts3694 for causes and solutions
If you're not able to restore the device, you should use: http://support.apple.com/kb/HT1808
Using that last article will erase everything on the device, so make sure you have a backup!
Good luck 🙂
Stijn