The POP3 specification mentions that a mailbox is locked while a client has it open. Therefore no messages can appear.
Think of this scenario: Most servers assigns new messages a low message number. You have just fetched all the message numbers:
1 - Foo message
2 - Bar message
You now want to delete the Foo message, but the server updates the maildrop to look like:
1 - Baz message
2 - Foo message
3 - Bar message
You send the command DELE 1, and have now marked the Baz and not the Foo message to be deleted. The POP3 protocol was developed when internet was a sparse resource and you were not always connected. If you want to have live updates to a maildrop, you should use the much newer IMAP protocol instead.
If you keep using POP3, you will have to disconnect and connect again to have updates. Notice that most servers does not allow clients to continue to connect/disconnect in a fast manner, they will simply reject your authentication if you are connecting too often.
Also notice that Gmail have a strange POP3 implementation. See What non-standard behaviour features does Gmail exhibit, when it is programmatically used as a POP3 server?