I have run into this problem a few times and think I may have the answer. If your Outlook says it's disconnected, and right-clicking the lower right and unchecking "Work Offline" doesn't work, this might help. This is mostly related to laptop/portable computers that use docking stations, because I have yet to see it happen on a desktop. That doesn't mean it can't though. If you have access to the email server, check the event log and you'll probably see some event 9646 in reference to the user in question. If you do, then this is most likely the fix
1. Open Outlook
2. Go to Tools->Account Settings
3. Choose the account you're having problems with, and click on Change
4. Click on More Settings
5. Go to the Advanced tab and uncheck "Download shared folders" and click Apply, then Ok
6. Click Next, then Finish
7. Click Close
You could also use Group Policy to enforce this on multiple machines. However, you first need to download and install the Microsoft Office 2007 templates on one of your domain controllers. Then add the Outlook template to the Administrative Templates section of the User Configuration section. From there the policy you want to define is User Configuration->Administrative Templates->Microsoft Office Outlook 2007->Tools | Account Settings->Cached Exchange Mode, and set "Download shared non-mail folders" to disabled. You can get the templates direct from Microsoft at http://www.microsoft.com/downloads/details.aspx?FamilyID=92d8519a-e143-4aee-8f7a-e4bbaeba13e7&displaylang=en. If you're not familiar with Group Policy, I'm going to have to leave that up to you to sort out.
This fix will not work immediately, but it should prevent the disconnect from happening again. The Exchange server's default MAPI session life is 2 hours, which is how long you'll have to wait unless you want to restart your Exchange services or modify the registry on that server. If you do need it to be relatively immediate and are willing to change the registry on the Exchange server, change the KeepAliveTime setting found in HKLM\SYSTEM\CurrentControlSet\Services\Tcpip\Parameters. It should be a DWORD with a default value of 0x6DDD0, which sets it for the equivalant of 2 hours in hex, measured in milliseconds. Change that value to something smaller, like 0x04650 (5 minutes in milliseconds, in hex). For more info, check out the last page of the TechNet article found here
You could also try setting up the user's Outlook settings in 2003, then migrating those settings to 2007. That has been successful for at least one person. To read more about his method, check out http://wtfiswrong.com/2010/03/outlook-07-disconnected, especially if the above does not work for you.
I also had found a forum where they had luck just flushing their DNS settings. This worked once for me, but then I found the other answer and that has been the only permanent solution I've seen. Just in case the above fix doesn't resolve your issue, here was the other possible fix I ran across:
1. Disable your Local Area Connection. To do this, go to Start->Network Connections (aka Connect To->Show All), then right-click on Local Area Connection and choose disable.
2. Open a command prompt. Go to Start->Run, then type cmd and press Enter
3. In the prompt box, type in ipconfig /flushdns and press Enter
4. Once that finishes, type in ipconfig /registerdns and press Enter
5. Once that's done, you can close the command prompt
6. Re-enable your Local Area Connection. To do this, go back into your Network Connections, right-click on Local Area Connection, and choose enable.
This problem (so I've read) is caused by a default limit imposed on the Exchange Server Outlook is connecting to. 32 is the limit, and once it is reached, you are not allowed to connect. Another potential fix for this is to change that limit on your Exchange server, but I provided the least intrusive fixes only in case you're someone that doesn't have control over your email server configuration.
For more information, check out Microsoft KB 842022. Fix 1, along with the server fix, can be found in that article. I had found a forum that said this was a known problem that was fixed in an update to Office, but the update wasn't being released until December 2008, which is still a few months away. For most of us that can't wait that long, hopefully this will keep us going until then.