1) Try using a new browser
2) Try clearing your cache and cookies
3) Check your email for any thing from FeralHeart
4) Change your password
If these don't work I'm sure some other people will have some ideas.
You can also try using a tab refreshing browser extension instead of a website and setting it to refresh the login page every 40 secs or less, I use Easy Auto Refresh for Google Chrome.
Edit: As for it logging you out in under 1 second... I unsure of what could be causing that but some browsers work better than others for certain things.
--Does it log you out while you are looking at it or when you open the game?