Cannot accept or decline invitations that come through Mail.

Finally I seem to have resolved the problem. Most likely due to a change in lOS or at AOL and Google, or all three, some point in the past, neither the Google nor AOL calendars were available on my iPhone or iPad. Apple support walked me through adding the Google calendar. AOL is more problematic, but I found an article in Support that details the steps to enable AOL: Adding AOL calendar to iPhone or iPad - Apple Community Even though I never use either Google or AOL calendars, they had to be enabled for the invitations to work.

One step the article doesn't mention is that I had to go into Settings> Calendar and make the AOL the default calendar since most invitations come to that email. Now when a meeting invitation comes to Mail, if l'Add to Calendar', I immediately get a Calendar inbox message that allows me to accept or decline it and a response is sent to the organizer. The event is added to my Apple iCloud calendar and is not greyed out.