Hello,
My first question was going to be did you call the ISP and ask if your client is breaking any sort of pop3 connections per minute abuse limit but you already did that Try calling them again, sometimes different first level support techs will know different things. Also, if they still say that isn't the problem ask to be be escalated to double check and verify this truly isn't the issue.
Double check the settings for all of the email accounts are correct and that none of the server names have a type-o in them.
Who is the ISP hosting the email? Is their pop3 port 110? If so...
When the problem is happening, from the clients computer try a :
Start -> Run -> telnet {pop.server.name} 110
Does that hang, come back with a response that looks OK, or is there an error message that can be used by the ISP to help troubleshoot the issue?
If there is an error please let us know the ISP, error message, and pop limit (if it exists) so the information can be used to help other people with the same problem in the future.
and Welcome to Email Questions!