To circumvence this behaviour there is an notes.ini parameter that may help. Use the following console command to set it:
SET CONFIG POP3_READ_ALL=1
This Forces the Domino POP3 server to present all available Inbox message identifiers to the POP3 client regardless of unread status. This puts the responsibility for determining what is new onto the client. If the mail profile is changed and the client-managed list (UIDL) is lost, any mail in the account will be downloaded again. If this is not set, reading a message with DWA causes the server not to present the message to the POP client.
If a mail was read in iNotes, the mail somtimes is not fetched by a POP3-Client. This switch overrides the problem.