Like Gertrude, I am baffled by this.
A POP3 server can only see:
1) The connecting client's IP address.
2) The login credentials.
The IP address will be assigned to the router/modem by the ISP, and should be the same for both the iPad and the PC.
If I understood right, all the login credentials work sometimes so they must be valid.
Frankly, it is hard to see how the server can tell the clients apart.
So if the email client reports a logon failure while another email client "is in mail mode" it should only be because your maildrop is already locked, ie the user is already logged in, or another user needing to access the same maildrop is logged in. If you can see a logfile somewhere, it would say something like:
-ERR maildrop already locked
The email client might well report this as a "login failure", or "wrong password", their error messages are usually rubbish..
But why would either email client grab and hold the server connection? Apart from the obvious (both clients are set to connect every few seconds) I can only think of scenarios with huge email attachments, slow antivirus checks and server time-outs.
Seriously weird!