Same problems here. Glad I'm not the only one.
After looking at the Activity window, this is what it displays:
http://screencast.com/t/NWU4N2Q5M
The Connection Doctor just says that all accounts were able to log in successfully, so no help there.
After clicking on the Stop Sign icon beside the stuff in the activity window (which effectively "stops" that task it's beside), I can then right click and "synchronize" my Exchange account and it receives all messages immediately, including the inbox. It's a work around, but I'm not sure that just command+Q and reopen wouldn't be easier.
It appears that a receive action just freezes up, which is why a resync before you kill the first sync doesn't fix it and a quit+restart does. As a side note, I can send messages through Exchange just fine when this receive lockup occurs.
Apple, please look into this...you have a better mail client than M$, but at least theirs stays connected.