I've double-checked my SMTP settings to make sure they're correct, and I've tried closing all other programs and even restarting the computer... restarting seemed to help in the past, but now nothing works. The other computer sharing the connection also has intermittent problems with sending e-mail, though not necessarily at the same time as ours (and it uses a different e-mail address). Again, no problems receiving, just sending.
This is so weird. And Sympatico's on-line documentation says nothing about this problem or how to fix it. Feh.