The default setting for most email clients when using POP3 is to
automatically delete emails once they are downloaded from the server.
So it requires your explicit setting to leave emails on the server, and
you would normally specify a period of time after which they will be
deleted automatically. Therefore if you are worried about emails going
missing, it would be better to use IMAP on all your clients (provided
that the mail server allows it; VM might not but others here will know).
Given that VM webmail shows you all the emails my suspicion is of
Thunderbird. In my very limited experience of helping others with TB I
found the display arrangements very confusing, with the same emails
appearing in more than one place; so it would not surprise me that there
is a similar confusion which hides emails. This of course would not be
improved by changing to IMAP but at least you would be more certain of
not losing emails by accident.
Can you set up TB afresh on a different computer (or on a different user
account) and see if it fails to show the same set of emails? That might
suggest that TB doesn't like something in those emails (malformed
header, large picture attached, identified as containing malware, etc.)
--
Graham J