I've managed to build up a few e-mail accounts that I use in varying amounts. Currently I have eight active mail accounts. Most are with one isp.
Mail seems to be struggling to manage all these log ins etc. First time I check mail on opening mail all accounts log on and download mail, but from the second attempt onwards two of the accounts refuse to work. Restarting mail allows me to log on again.
It's always the same two accounts so the problem may be at the isp end but it's strange that a restart of the app always fixes it (once)