Mail.app keeps asking for Google password I've a Google account set up on a Mac of mine. OS X version 10.8.4 and everything else is up-to-date. And my Google account uses 2-step authentication.

I'm having a problem with my Google account on this Mac in the native Mail app. The problem is that when everything was working fine, one day, all of a sudden Mail asked for my Google password. I simply created a new application specific password. But after some time the same happened again and I ended up creating another application specific password.

Now it's happening again and it's kind of getting annoying.

Why does it keep asking for passwords when the one before was right and working? Has anyone else ever had this problem?

Also I should mention that my iCloud account, also set up on this Mac, functions perfectly.
If you have several devices accessing your Google account via IMAP you can reach the limit of connections Google permits. The limit is 15 connections per account, however, bear in mind that each client can open multiple connections. In my experience the limit is easily reached with 3 devices. I have read that the Thunderbird email client has a setting to specify how many connections it can open, Mail and Outlook do not have this option.

Your Mail client should prompt you with a message along the lines of "Too many simultaneous connections." However I believe on iOS devices and Apple Mail you may see a more generic error. 

The workaround for this issue is to log in to the GMail web interface, scroll to the bottom of the page and click the 'Details' link. From the popup window click 'Sign out all other sessions'

support.google.com/mail/answer/97150?hl=en