I have an iPhone 4S and wanted to upgrade to OS 6.0. The OTA update failed. I plugged in cable, pointed to the OS6 IPSW and tried to do an upgrade on the jailbroken 5.1.1. (Didnt care about losing the jailbreak). The update failed with an error 6. It then restarted into a recovery loop.
I tried to kick it out of recovery with TinyUmbrella, RecBoot, RedSnow as they have a soft kick out of recovery option for the 4S, neither worked. I tried various other tools without success.
Moral of the story, it appears that iPhone 4S 5.1.1 jailbroken will go into recovery loop when updating.
I didnt think to backup beforehand because I thought an upgrade would simply upgrade and wipe the jailbreak data. Not the case apparently.
You can try and put the phone into DFU mode to see if it will update, however not sure if it will work. I would try and download a new iOS. Otherwise the discussion of jailbroken devices is not allowed.