I am having a similar problem with Facebook loading. It has loaded normally a couple times, but each time I have to re-enter my password. More commonly and it does one of two things:
-- logs in and then immediately logs back out (not touching the screen, password verified correct, no special characters)
-- OR i enter log-in info and the logging in message spins and spins and spins. (I've not waited it out to see if it eventually resolves)
Settings for Facebook
Alerts both ON
Push Notifications all ON
If anyone finds a good solution or is using different settings that work, I would love to hear your input!