Apple released the iOS 6.1 beta 2 build 10B5105c firmware to developers moments ago and sure enough iH8Sn0w has tweeted when the beta firmware expires. According to iH8Sn0w the iOS 6.1 beta 2 firmware will expire on December 28th, 2012 at 12AM (GMT).
Apple implemented expiry timers on beta firmwares to ensure developers who update to one of the beta firmwares either upgrade to the next beta or the official firmware when it is released. If you do no upgrade to the next firmware version in time your device will be placed in Recovery Mode.
Not much is known about the iOS 6.1 beta 2 firmware at this time, and only developers should be updating their devices to it. There is no reason for non-developers to update to this beta firmware as no exciting new features are present except movie ticket purchasing through Siri.