iOS8.1 Can't stay logged in to Stack Exchange or Stack Exchange chat

So everything was wonderful before iOS8.1. Now I can no longer log in to Stack Exchange via Facebook on Safari (diagnostics say it's an HTML 5 issue), but can log in via Facebook on Chrome or via Stack Exchange on Safari. However, if I leave the screen, either going to another Safari tab or another app, I have to log in all over again. This never used to happen in "the good old days."

I gather Apple is still not fixing all the things that are broken in Safari (for example, certain videos won't even load or play). I went to the extent of completely reinstalling the iOS via iTunes.

I'm running one of the early iPad minis (fall 2012).

Any ideas?