IMAP accounts locked out - small triangle lock error symbol

Question

I use Apple Mail to read several Gmail IMAP accounts. Mostly, it works fine. I've used Gmail IMAP since IMAP was offered.
Every so often, one or more of the accounts will lock out. Apple Mail will display a small upward pointing triangle error symbol enclosed in a small circle, next to the account name. When I click that triangle error symbol, it explains "There may be a problem with the mail server or network. Check the settings for account. The server error encountered was: Too many simultaneous connections. (Failure).
I have 6 IMAP accounts connected, but I hear other people manage that number fine.
The largest IMAP account has around 3GB of data, and I've heard that people get to 6GB with Apple Mail handling that well.
So I don't know why this happens. It is intermittent.
Using the latest 10.5.7 Leopard Mail.

Answer 1

The too many simultaneous connections is from gmail, not Mail. Google limits the number of simultaneous connections to their server to prevent someone from hacking into your gmail account. It mostly prevents me from reading my email.
When Mail opens a connection to an IMAP account, it generates multiple connects to allow real-time, upload, download, sync, etc. instead of one connection that must wait for the others to finish. Depending on the positions of the Moon, Sun, and Uranus, Google will identify this as too many connections.
I can usually unlock it by logging into the gmail web interface. I'm not sure why adding the connection clears up the other connections, but there you go.