How does one update a Jailbroken 4S on 6.1 to 6.1.1 and preserve their jailbreak?
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.