Stolen from another forum...
"I have been locked out of my account for two days and suddenly it worked for me last night. Here is what I did to fix this problem. 1.) open the app and logout from the account 2.) start a new game with a new email address (you can tell if it's a new game from the introduction video where homer blows up Springfield) 3.) once you have played the new game long enough, you should be able to tap on the Bart and Milhouse icon. 4.) then you tap on the origin icon on the bottom left hand corner of the screen and logout from the account 5.) login into the account that you have trouble logging in with and it should work
I also have tried leaving it on but I would just crash after 10 minutes. Logging on an iPad didn't work and I don't know anybody with and iPhone 5.
Hope this will help you guys."
Hope that helps.