We have found the problem.
VPOP3 is first trying to connect using SSLv2. (This protocol isn't secure, so *most* servers will reject this attempt).
With one server, the server is saying 'no, try TLS1.0 instead', so VPOP3 connects using TLS1.0 and all is good
With the other server, the server is saying 'no, go away', and is then closing the connection.
If you tell VPOP3 not to try SSLv2, then you should be OK.
To do this, go to a command prompt in the VPOP3 directory and run
vpop3settings set sslclientallowsslv2 0then restart VPOP3
VPOP3 has SSLv2 enabled by default for connections to remote servers because a few remote servers still require that. The ones which don't allow it usually tell the client to try something else instead, which is what the first server is doing. I don't know why the second server is dropping the connection instead of getting VPOP3 to try something else.