Turn on logging for the problem account. See http://reddit.com/r/operabrowser/wiki/m2tips/enable_logging.
Look for errors yourself or zip the log up and provide for download somewhere so we can look at it.
Also, download the Opera installer, launch it, click "options", set "install path" to a folder on your desktop, set "install for" to "Standalone Installation (USB)" and install. Set up the IMAP account in that Opera Mail and see how things work there. That will rule out a problem with your mail folder in your original Opera. If you get no problem, switch to "make all messages available offline" and see if it then causes problems. If so, it might be the body of a single message that's causing the problem. What message Opera stops at in the log might reveal the problem message.
Another thing you can try is to close down Opera and edit incomingN.txt in the mail folder where N is the number for the account as seen in accounts.ini. In there, set Force Single Connection to 1. See help -> about Opera for the location of the mail folder.
The outlook servers have been known to disconnect Opera for no reason, so keep that in mind.
Also, on the "Incoming" tab in the account's properties, make sure "include this account when checking manually" is checked. Make sure "check for new messages every..." is checked and make sure it's set between 9 and 31 minutes.
Also, if syncing messes up, try clicking the drop-down next to the check/send button and choose resynchronize.