Hi Aida Jolley,
Thank you for the reply. The e-mail account in question is IMAP, i.e., it uses a .OST file. I have completely blown away the .OST and let Outlook rebuild it from scratch. The problem remains. I have found a couple of interesting new facts about the problem:
1. The e-mail does get sent despite the error.
2. The e-mail remains in the outbox (it can't be resent without using the "Actions>Resend message" path)
3. I can drag it to the Sent folder (which is on the server) with no problem.

The error message describes two possible causes: "Outlook is offline or the e-mail server doesn’t allow items to be saved to the Sent Items folder." Clearly Outlook is not offline since the e-mail does get sent. Equally clearly, the e-mail server DOES allow items to be saved since I can drag the e-mail there after the fact.

However, I think there is something flaky with my system's perception of the Internet connection because sometimes Microsoft store says I am not connected to the Internet during an install or upgrade. (If I retry it generally works on the second try; always by the third try.) I don't believe there is anything wrong with the Internet because none of my other systems complain and I can access the Internet with them while this is going on.

This all started when I upgraded my Win-7 OS (barnacle-encrusted after being active for two plus years) to Win 8.1. I did this by installing Win 8 from scratch (not upgrading) and then upgrading to Win 8.1. This "OS Reinstall" has gone somewhat smoother than past re-installs except for a few anomalies like this.

Bottom Line: the problem still exists.