These errors occur whilst VPOP3 is communicating with your ISP's SMTP mail server to send your mail.
If the message text is:
Error with SMTP Client (XXXX (YY)) The server connection was closed unexpectedly
Then this means that the the connection between VPOP3 and your ISP's SMTP mail server was closed when VPOP3 did not expect it to be. This can be caused by the network connection failing or a bug in the ISP's mail server which drops the connection in abnormal circumstances.
Following this text there should be a further description of the specific error which occurred. See here for a description of those errors.
If the message text is
The VPOP3 SMTP Client (XXXX (YY)) has encountered an error whilst retrieving messages from your ISP POP3 server The received error was: "ZZZZZ" The last command sent by VPOP3 was: "WWWWWWWW"
This means that your ISP's POP3 mail server returned an unexpected error response when VPOP3 sent a command. 95% of the time these errors are caused by problems with, or bugs in, your ISP's mail server, so we recommend that you contact your ISP if the situation is not mentioned below.
Note - unfortunately the error code number (eg 503, 525 etc) does not define what error has occurred, it just indicates the type of error (eg a 5xx error means a 'permanent' error). Most mail servers will give some human readable text after the error number, this gives more information about the error.