After downloading large # of mails, Gmail POP downloads only one message at a time

Another thread on Gmail forum has the correct solution.

I resolved this issue as well by following what ant0nis did. Uncheck "Leave messages on the server" in Thunderbird, but LEAVE "When messages are accessed with POP:" to the setting "Keep Gmail's copy in Inbox"

GMail's setting needs be "Mail Settings" -> "Forwarding and POP/IMAP" -> "POP Download" -> "2. When messages are accessed with POP" -> "Keep Gmail's Copy in the Inbox". This setting ensures that the mails don't get deleted from your account even if they are downloaded from a POP email client.