could it be you have consumed the allowable 5 concurrent connections on a single mail server? That is are they all say @gmail.com email addresses? There is no practical limit, but if you have say 5 accounts checking for messages every minute I could see exactly what your a saying happening. The sixth and subsequent connection attempt failing. I see this occasionally on Startup with outlook accounts.

Fundamental email is not an instant messaging platform, despite a lot of people acting like it is.