I have a user who's using Outlook 2010 (Greek) to read his email from a POP3 (perdition in front of an ipop3d / UW-IMAP server). A few days now we're observing the following behavior:
Outlook when started tries to download new email. It (very slowly) downloads headers from all the messages and then starts to download messages. Some messages before finishing the download it fails with error 0x80060040. No new messages are shown to have been downloaded (not even those for which the counter was counting them as downloaded).
In case it matters, the user's .pst lives on an external USB disk and is over 3.5G.
I don't have an Outlook 2010 client in front of me, but try creating a new PST file and setting the delivery for the POP3 account to that PST instead of the original. Worst case is you'll have 2 PSTs in the profile, which is probably a good thing considering the original PST is getting out of hand size-wise. Another thing you could try is moving the PST to another disk and re-targeting it in the Outlook profile. Maybe the USB disk is out of free space?
If you haven't done so already, I suggest:
It might be possible that your usb drive is dieing and that the pst file is slowly getting corrupt.
My advise. Like Clare Macrae said, but slightly different: repair the inbox and move to your local drive.