I ran into frustrating issues such as outlook only partially updating my Inbox, or completely getting stuck and not updating at all. I'm connecting to Exchange over HTTPS.
Reducting (rather drastically but well) my MTU to 1024 solved the issue instantly !
I'm not sure if it has to be done in Wine (I did it by creating HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\Tcpip\Parameters\MTU with regedit, the keys Tcpip and Parameters didn't exist, nor the DWORD MTU).
Anyway, I also did it on my system (ifconfig eth0 mtu 1024, careful it's not persistent, only for test for now).
I restarted Outlook, and it happily downloaded all my stuck e-mails :)
Hope that can help somebody else !
Alban