From: DeskNow Knowledge Base
http://www.desknow.com/kb/

Some user accounts do not receive email automatically from External POP3 account, even if 'Check automatically' is enabled
http://www.desknow.com/kb/idx/4/123/article/

When there are problems in receiving emails from external POP3 accounts, the following log files should be investigated:

log.ExternalPOP3

log.MailIngestion

If log.ExternalPOP3 reports an error like 'Remote POP3 server said: ERR POP3 - server reached max email connections' or anything similar, then the problem is that you probably have many external POP3 accounts on that server. To speed processing, DeskNow opens multiple connections to that server, and maybe that server cannot handle all those concurrent connections.

In this case, the solution is to edit Mail.cfg and change the line

ExternalPOP3.fetchThreads 20

to a lower value, ex:

ExternalPOP3.fetchThreads 4

This will force DeskNow to use less connections, and probably the remote server will be abe to handle all of them. Restart DeskNow after the configuration change.