This hassle began for me on 8.8.12 in the afternoon.
I have an iPad and and iPhone out of commission with "imap.gmail.com not responding" server issue.
I have 2 desktops (1PC + 1Mac). Both are fine accessing the same gmail account the iPad and iPhone can't access. Very weird.
Like others, nothing has changed about my password and I had not fiddled with 'Settings.'
Based on other forum input, I added a server to my mail settings: imap.googlemail.com : -() No luck.
Since we can't call Google, hope to find a solution here soon.... : -)