The file \Data\profile\Mail\pop.[mailserver].[domain]\popstate.dat file is what keeps track of which emails have already been downloaded from the POP server.
An example on my Windows XP Home PC is:
C:\Documents and Settings\Alan\Application Data\Thunderbird\Profiles\qn5qd3de.default\Mail\pop.att.yahoo.com\popstate.dat
# POP3 State File
# This is a generated file! Do not edit.
*pop.att.yahoo.com AWehmann
k AHfVimIAAFFZTwJOOAAQHz0XYU8 1325822549
k ALnPjkQAARslTk0SJwOBFFSXUwk 1313674828
k ALbPjkQAADijSiRISQK9whTL178 1243891806
k AK/VimIAAXI5TwSSMQM8WDKNut0 1325822555
k ALDVimIAASYOTuZNwgVwMgSXZN4 1323792415
k AN7VimIAAM1uT0ZHUA1JGhbBzms 1330020393
b AODVimIAAQzKTuDXaAISoH6BC8M 1323402949
There are more entries, but I don't show all of them.
The column #2 has email IDs, column #3 has the email dates in unixtime format (use a tool to convert to human-readable or back).
By deleting appropriate lines you can make Thunderbird re-download those emails.
In your case, as Thunderbird has the IDs already, it should not re-download these emails.
In the case of Gmail things are somewhat different. With default settings the Gmail POP server only offers newly arrived emails. If there are none, then the popstate.dat file is emptied out, since the server reports that there are no emails available for download from the server.
Best Answer
They are most likely marked as "Read" already on the email server. Go to the email server and attempt to mark all of the emails as Unread. This will then allow the client to download them.
The client doesn't want to download emails you have already seen/read.