Suscribe2 service is now restored and I wanted to share with my findings. (It's a bit long, but I tried to give you every detail that might shed light on the nature of the problem.)
Earlier on, the daily digest didn't go out (for 2 weeks), and last time even the Send Mail feature failed to go out and generated the following error message:
Message failed! Check your settings and check with your hosting provider Could not instantiate mail function.
OK. I spent lots of time on this: Re-setting up WP, fixing the database, talking with Level 2 hosting support... Still, no change...
THEN, I called the host support again and went over their main error log for the website (not site-generated php error log, but the errors their various system record). The guy noticed an error stating that an email address (to which the dispatch was being sent) of one of the WP *users* (whose email account hosting is provided by the hosting company) was rejected as non-existing.
That address was about 10th on the list of nearly 400 addresses (which is well under the limit of total addresses sent at once). I deleted that address from the Subscribers list and tried re-sending the special mail message ("Send Mail") to the list, and it went out perfectly.
Which, I think, means the following: In version 8.8 and 8.9, when an address is rejected by the server, the plugin is stopped -- at least that's what happens when the rejected address is of a WP User who's on the distribution list and the host system generates an error. (I'm not sure the host's system would generate an error if an address is rejected by another mail system...)
(I'm saying version 8.8 and 8.9 because we had the invalid email address for many months, and the problems I report here started recently. Now, at the top of this problem report I said that I had the problem under version 8.8 as well... but, honestly, I don't remember just when I upgraded to 8.8... So, I might be off on the version numbers, but it surely includes both 8.8 and 8.9.)
My guess is that when an email address is rejected by the host, all the names *following* the rejected address don't get serviced.
I'm sure you'd know whether this is something that you can fix or change in future versions, but something should be done -- email addresses get rejected all the time and I think this is bound to happen again, and to many others, no?
Lastly, another matter, not related to this problem:
Since the service was restored, the digest email FROM field is not the WP user whose email address was selected (as was always the case before), but the the hosting master account (of which this web project is just one sub account). Do you have any idea why this is happening? Could it be an empty field or entry that I left out when configuring the current installation of Subscribe2 ??? If so, where do I look for it?
I hope the detailed report helps you figure out why we had this problem, and improve the plugin.
Thank you again for all your help!