Woow, the level of reading comprehensions on this forum is astounding.
The OP is now on 6.1.3 after a restore. If restoring the phone does not help remedy the problems the OP should go to the Apple store to have his/her phone diagnosed.
The OP is under no obligation to mention jailbreaking as he/she is not experiencing the said problem on a jailbroken system but on a official unmodified version of the iOS.
It's completely up to Apple to help the OP or deny him/her service.
" ...Apple
may deny service for an iPhone, iPad, or iPod touch that has installed any unauthorized software."
Source:
http://support.apple.com/kb/ht3743
Most people if not all who bring their iPhones to the Apple store have them repaired or replaced as long as the phone is still within the warranty period and shows no physical or water damage.