Thanks for the help. It kinda works. See below.
Originally my WinGate email/servers list contained one line, listing my ISP's mail server, no login required, port 25. That worked fine until I added a second ISP and a second WAN connection (my Netgear FVS124G supports two WANs). Then sometimes the outgoing email would go out on the second WAN, and my original ISP would refuse to accept the email since it was addressed to his server but didn't show up on his wire.
Sending outgoing mail to the mail server at my domain seemed to solve that problem. I changed to WinGate email/servers list as you suggested, to remove the ISP and add my own domain, complete with the necessary login. Three cheers! Unfortunately, the same problem came back today, which probably means I "solved" the wrong problem. The bounce message (from MS Exchange 5.5) looks like this, with a couple of edits for privacy:
********************************************************************************************************************************************
Your message did not reach some or all of the intended recipients.
Subject:
Sent: 1/1/09 8:18 PM
The following recipient(s) could not be reached:
gallowaygold@xtra.co.nz on 1/1/09 8:18 PM
Unable to deliver the message due to a communications failure
The MTS-ID of the original message is: c=US;a= ;p=John;l=JOHNS-090102041811Z-52
MSEXCH:IMS:John:HOME:JOHNS 3553 (000B09AA) 553 <John@mydomain.org> is not allowed to use this service
*********************************************************************************************************************************************
Adding to my confusion the problem is intermittent. I suppose my domain host could be having problems, but they've seemed quite bullet-proof over the period I've been with them. Anyone's thoughts would be appreciated.