Well, if you go to the menu bar in Mail->Accounts you can adjust 4 checkboxes for each gmail account. So, why not the 6th gmail account? That question I had gave me an idea. It would happen after Mail.app was hidden for approximately 2 or more hours. FINAL UPDATE: After doing alxxhrvth's 4 steps a couple of days ago (as I posted about a few replies ago), I still ended up getting the offline indicator for 5 of the 6 gmail accounts that I re-added to Mac Mail.