If you just turned on Google’s 2-Step Verification, and your iOS device keeps asking you to reenter the password, follow the instructions in this article to get Google’s 2-Step Verification to work with the Mail app on an iPhone or iPad.

I think you can also get this to work by changing the account type from exchange to gmail. We originally set our accounts up as exchange accounts in 2012, because that was the recommendation. I don’t think it is any more.