Error 10503 means that the connection between VPOP3 and a remote computer (normally your ISP) was dropped at an unexpected time. This is different from the error 10054 in that this is a controlled line drop.
One way this can happen is if the ISP's POP3 server uses an obsolete standard which allows it to drop the connection if a POP3 'LIST' command is performed on an empty mailbox. The current standard requires that the connection is not dropped until the client (VPOP3 in this case) performs a QUIT command.
We have established that some ISP POP3 servers using the QPOP 2.53 server software (a popular Unix/Linux POP3 mail server used by many ISPs), or custom mail server software based on that software, are closing the connection immediately after a connection from a client computer without reporting any POP3 error message, causing VPOP3 to generate a 10503 error.
This appears to be a load problem on the ISP server, and only happens when the ISP's mail server is very busy. If this happens then subsequent connections may work OK, so it is usually not a critical problem as mail is still delivered OK (eventually). This problem it is not exclusively happening to people who use VPOP3 to download from QPOP servers, it also happens with people using other download software. It may just be more noticeable with VPOP3 because it usually connects many times a day, and reports the errors in an email message.
See also Timeout Problems When Sending or Receiving Attachments