1. Our Google Apps users with the issue, all have 2-factor enabled. We use Centrify to push the Mail settings so that when a user logs into Centrify, it gets a payload for Exchange settings, which in turn uses the user's email address as the username, and the Exchange settings for Google, like 'm.google.com' for the server name. All users are using the standard iOS Mail account to manage their email.
This issue just happened again, about 1/2 hour ago, but not to all users, which is strange.
We also noticed today, that there seems to be a duplicate setting when you go into the Mail settings, it looks like there are two payloads being delivered (i.e. Setting, Mail, Accounts, "Name of our Payload" delivered via AD/Centrify). When the app specific password is entered, the 2nd account goes away.
2. I am not sure about this - the symptom is that all the users contacts, emails, etc go away. I'm not sure if they were attempting to access the Mail.app or not.
3. Yes.
Thanks for the info on capturing the logs.