Do you have more than one pop mail account with different ISPs? If so, your current (the one you pay each month) will let you receive any pop mail addressed to you. However, many ISPs don't sending mail from another ISPs system through their server and will reject it. Happened to me and took me a good while to figure out what was wrong (this was using Thunderbird, by the way). Example:
tries to send an email from bob@secondISP.co.uk
through firstISPs servers. Won't work, mail is rejected.
This may not be your problem because you did not mention multiple addresses. Thought I would mention it as a possibility with Thunderbird.