Wow, I hope they're paying you well. Generally you would double check the settings on both ends, at the exchange server compare the problem account with one that you have confirmed to be working in both directions. Then on another client machine that Outlook is known to be working on, check all the account settings and compare them.
Here's a link with a walk through that might help Link Removed due to 404 Error
although I noted that he recommends checking the box for "Use Cached Exchange Mode in step #4, while others have reported that unchecking the box resolved problem that they were having. That's another reason why I suggest comparing settings between a known good account and the problem account to determine if there are any discrepancies.