Mail.app does not fetch mail regularly with Exchange accounts on Lion
This is a problem with Mail.app on OSX Lion which affects Exchange accounts only when Mail rules are enabled. All other IMAP/POP accounts work fine with rules. The "fix" I received from my sysadmin was to disable Mail rules — a bit harsh, but in the end I ended up implementing the same set of rules (mostly moving to different mailboxes) server side.

Digging further into this led me to this thread, and it seems the issue, while observed among Exchange users, has also affected others. Some of the suggestions there that worked were (not counting highly specific ones):


Delete all rules that were formerly in Snow Leopard and recreate them from scratch in Lion.
Use MailActOn, a paid app that costs US$25 to set up your rules. Several users commented positively on its usefulness.


One thing in common with nearly all the complaints there (and mine) are that the rules involve moving messages to different mailboxes. Simpler ones like highlighting messages still work (for me too). So until this is fixed by Apple, I'd recommend implementing rules that involve moving mails on the server side or using the app above.