I suspect that this has nothing to do with the web interface, but rather the EV server talking to the exchange. What version of EV? Does it clear up after a service restart (5.x) and/or a reboot?
You may have too many MAPI session defined, EV creates them automagically.
While logged on as the service account - If you look at: HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\Windows Messaging Subsystem\Profiles\
You will notice how many you have.
You can edit the registry of the EV server to cleanup more aggressively by creating a DWORD "ProfileExpire" under HKEY_LOCAL_MACHINE\SOFTWARE\KVS\Enterprise Vault\Agents\
I have set this to "3" in the past which cleans up profiles that are 3 days old.
Lots of other MAPI errors possible though, so post some more info.
A