Can't send mail - server properly configured and up

Question

I'm unable to send mail. Here's roughly the sequence of events that
got me where I am:
1) Connect through a firewall using VPN (the Cisco VPN client)
over the wireless interface
2) Compose a message, and click 'Send'
3) The server is down, so I get the "Can't send e-mail" pop-up
dialog
4) Click 'Try later'
5) Reconnect later while the server is up, and try to send
6) Still see the "Can't send" pop-up
Steps 3) and 4) happened a lot. In particular, turning on the
wireless interface in order to connect over VPN causes Mail to try
(and fail) to connect to the server.
The server is up; I can reach it with "telnet <server> 25".
Moreover, Mail's own "Connection Doctor" says it's able to connect
to the server.
This configuration worked until the sequence of events described above,
and nothing on the server side has changed since.
I've tried everything I can think of to get Mail back in a working state.
Notably I've deleted the contents of "Outbox", quit Mail, and then restarted.
I've also deleted and re-created the server configuration, without success.

Answer 1

Two additional data points:
1) I found a mail server I could use from outside the firewall.
When I added that server, and closed the VPN session, Mail was
(finally!) able to send. (But see below why you shouldn't rush
to blame VPN).
2) When there are two mail servers configured in preferences, the
"Can't send mail" pop-up gives you the list of choices. If you
select an alternate server from the list, the "Try selected
server" button ought to try the new server. Instead, the
pop-up reappears, still complaining about the old server.
As for why I'm not prepared to blame (only) the VPN:
* Note that the server is perfectly accessible; telnet works,
and Mail's Connection Doctor says the server is up.
* Point 2) above indicates some problem in Mail with the logic
for retrying access to the failed server.