How does one update a Jailbroken 4S on 6.1 to 6.1.1 and preserve their jailbreak? I'm running a iOS 6.1 on a jailbroken iPhone 4S. I was one of the many to jailbreak my phone when evasi0n came out. As some of you may know, Apple has released iOS 6.1.1, an 'emergency' update for some battery and other issues experienced on the 4S. I'm one of those affected by the battery issues (its not the jailbreak's fault, I'm very conservative with what I install).

I'm hesitant to just hit update in iTunes. Do I need to restore my phone first to a fresh 6.1.1, restore all my data then re-jailbreak? Am I going to have to install all of my tweaks again? Thanks for any input on this.
You need to restore the device to install a clean version of iOS and then re-jailbreak (OTA updates simply do not work and using the update feature in iTunes can leave behind data that will eat away at your disk space).

It is actually good form to set the device in DFU mode (rather than just hitting restore in iTunes) and then let iTunes take it from there. Once the device is upgraded to 6.1.1 and jailbroken, you can then safely restore from your backup.

Your question (and many additional topics related to jailbreaking) is actually covered on jailbreakqa.com, the official information and help site for jailbreaking.

You cannot "preserve" a jailbreak.