[whpalmer4]

Hmm. I have 2 iPads, an iPod touch, an iMac and often a MacBook all banging away on my gmail account (IMAP), and I haven't ever seen this error, nor does Mail.app ever "lose the connection". I find it very reliable for doing just what you describe.

One suggestion is to set up another gmail account, configure it only on the Mac Mini, and use it as a receive-only address for getting items into OmniFocus. That should largely eliminate any justification for getting the "too many connections" error wrt that account.