Mac Mail "Not Responding" with Gmail IMAP account I'm experience some issues with my Mac Mail on my MacBook Air.
I hasn't been there all the time, as far as I can remember it started around Yosemite.

In my mail, I've two accounts. One is my work mail which is an IMAP for Google Apps gmail and the other is my private mail which is just a standard Gmail, also with IMAP.

On my private mail I've two-factor turned on, while this is not the case with my work mail.

Now, seemingly random my Mac Mail gets non responding and I've to hard quit it and reload it. It has something to do with the synchronizing and my private mail but can't seem to figure out what.

I hope someone has a solution or has experienced this before and know what to do.
I rather not turn of two-factor of my private Google account if I can avoid it.

Cheers
Do you have a Google "App password" set up?  If not, you need one.  This thread has a lot of information about how to do that: How to setup Gmail SMTP server for OSX Mail with 2-step-verification and App-specific password?

If that is not the problem, it may be that the Yosemite upgrade broke it.  I posted a detailed list on the apple forum of steps I took to fix a similar problem.  Although I am not using two-step verification, some of these steps might help you, because there seems to be some significant issues with Yosemite upgrades "breaking" Mac Mail.  I didn't use detailed instructions regarding navigating to all the settings; if you need assistance with that, reply here, and I'll elaborate: https://discussions.apple.com/message/28551720?tstart=0#28551720