Download the Opera Mail installer, launch it, click "options", set "install path" to a folder on your desktop ("test Oper" for example), set "install for" to "Standalone Installation (USB)" and install. In that Opera, set up your POP account (just don't uncheck "leave messages on server" in the account's settings) and see how things work there. If they work fine, you basically just need to rename the "mail" folder in your original Opera Mail profile and set up your pop3 account again to fix things.
If you plan on fixing things with your original Opera Mail profile and you have messages stored in Opera that are no longer on the server, you can use "Menu -> settings -> import and export -> import mail -> import generic mbox -> add folder" to import the old messages from the renamed folder (the store/accountN folder in the mail folder where N is the number for the account as seen in that mail folder's accounts.ini) into the account you just set up again. Then, if you have any duplicates, you just delete the imported copies and keep the copies freshly fetched from the server.
Or, if you just want a quick fix, you can rename the uidl file in the pop3 folder in the "mail" folder. That should cause Opera to fetch all messages in the Inbox again and things should just work fine.
It could be a certain message in your inbox though that's messing with Opera. You could log the connection to see if you can determine what message Opera stops it. Then, you can move that message out of your Inbox via IMAP, or the webmail interface (if there is one).