Apple pushed iOS 8.1.2 last night citing fixes for issues relating to purchased ringtones disappearing. While this usually means bad news for jailbreakers, we can confirm that iOS 8.1.2 does not break the kernel exploit that allows for an untethered jailbreak and TaiG has been updated to v1.2.0 to support iOS 8.1.2
You can download Taig from here and enjoy the latest update for iOS with all the jailbreak perks!