One address uses eStreet in Denver and at some previous time Acronis was successfully issuing alerts on that account. Although the mail server has since changed--which should make no difference.
The other account is Gmail so Google is the ISP.
As I mentioned before, the ports and security match that of Outlook. With all the problems I was infinitely triple careful entering and checking the values.
Further, we're talking 2 computers, 2 versions of Acronis and 2 addresses per computer. I'm not a math whiz but the odds of at least 1 alert functioning should be fairly high.
I posted this problem on the Acronis forum a long time ago to no avail.