By default on Windows, POPFile can only download mail from one POP account at a time. If your client is attempting to get mail from several POP accounts at the same time, connections must wait their turn. Mail clients wait for a while, but sometimes the connections for the later accounts may timeout before POPFile can get to them.
If the number of accounts you are checking mail for is causing trouble you will need to enable forking. Forking has been known to sometimes cause trouble on Windows so by default it is not enabled. To turn forking on, go to the Advanced page and change pop3_force_fork to 1, then restart POPFile.
You may find that turning off the tray icon improves other problems forking may cause. Other than that, you will have to just not check all your mail through POPFile at the same time.
Forking currently cannot be used with the SSL module, so if you use SSL to connect to any of your accounts you can't use forking.
The first option is to drop email addresses you never use or at least don't run them through POPFile. Lots of us have lots of addresses and never really do anything with most of them.
Another option is to collect all the mail at one (or a few) of your addresses. Many services let you forward or redirect to another email address. Others let you set them up to download POP mail from other accounts (a few times a day usually). If you somehow pay for the account (ISP or webhosting) one or both of those options is usually free. Free accounts may let you forward for a yearly fee.