I could be wrong but it sounds like a limitation of Eudora if you have to use one login for both sending and receiving.

If you need only one pop server to receive from, and only one smtp server to send out through, then don’t name any server with the pound sign in the Eudora setup. Just use your normal logon name and specify 127.0.0.1 as both the pop server and the smtp server. Avast will contact the appropriate server for sending or receiving as specified in its INI file.

If that doesn’t solve your problem, try a different mail client such as Pegasus or Thunderbird et al which allow separate login setups for pop servers and smtp servers.