shai> drush up drupal-7.28
I'll return to the above suggestion in a moment ...
Well, I waited a day or so, and the 7.28 version eventually appeared using the simple "drush update" command. So, I've updated successfully.
I didn't use your suggestion (explicitly specifying the version) since my "usual" way *should* have worked.
I ask again: why didn't the second site show up as upgradable on that first day. Doesn't Drush access the same server (I assume on drupal.org) no matter from which site "update" requests come?
Though I am again a "happy camper", I am just trying to understand what was going on - or not going on - as the case might be ...
Thanks for all help,
-Kenneth