Your server administrastor has limited the number of items you can open simultaneously

What version of outlook are they using?
What version of exchange are they using?
What version of the client are they using?
Have any of the users reported this more than once or is it different users?

If its the same select group of users would suggest setting client logging to full so next time when it happens you have something from the client that may provide whats going on

I know there was an issue with outlook 2010 and too many folders would hang the client, but i don't remember it giving any specific error, but the fact that it trawls through each folder for different reasons, it could be that exchange is rejecting the requests due to too many simultaneous connections (probably because people used to set up Indexing on their desktop and bring exchange to its knees as it trawled the exchange servers)

What i would suggest is upgrading to the cumulative hotfix, although it says Public Folders, it may resolve mailbox issues as well

Also googling around based on "Your administrator has limited....." seems to show that your exchange admins may have placed a limit on MAPI Connections, I know in Exchange 2010 this is set by default to i think 32 which is why that powershell script has to be run to stop any errors....in Exchange 2010 its called "Throttling"

If you look on the Event logs of the exchange servers do you see any Event 9646? This should be logged when a user gets that error message, will also give you an idea of how big in scope this issue is.

So it looks like the EV Client is going nutso when scanning the mailboxes (For whatever reason) or it could be a combination of EV Client + AntiVirus + Indexing, however by defauly the limit is 32 mapi sessions so i'm not sure why any of the clients would need more than 1 anyway!