richard, yes I understand.
RIM has this KB article you might review... although it does sound like you have it set correctly.
KB12283 KB12283-How to leave or remove copies of email messages on the messaging server
So, I might ask this, if you turn OFF, or close Thunderbird for a day, and it does not download ANY email to Thunderbird, then does your BlackBerry get the mail correctly?
In other words, let's test to see if Thunderbird is the problem here.