Apple Mail requesting password repeatedly when server load is high

When load on my mail server is high, I see a lot of Mac clients (OS X Tiger with Apple Mail) start asking for the user's password. Usually, they can hit cancel and then take the account "online" and they are fine.

It looks like the timeout for connecting to the IMAP server is set a little low. Is there a way to configure a longer timeout period for Apple Mail? I have been hunting around the GUI, but I can't find anything. Other mail clients don't have this problem (I tested with Thunderbird).

Any advice would be welcome, cranky users are banging at my door.

Thank you,
-- Miles