If the normal state of affairs is low activity (days per post rather than posts per day) then it's going to be difficult to prove that the current hiatus is part of a downward spiral rather than a normal pause in activity. You need more data that doesn't rely on actual activity (posts/votes/likes/etc.)
Perhaps the only way you can do this is to log all visits to the site - no matter what page the user lands on or how long they stay on the page.
If the community is still "alive" you should see people visiting the site and reading a few pages even if they're not posting new content. If they're still interested they will be visiting to see if anyone else has posted something new. If people aren't even visiting then is the time to get more concerned.
Now, if even the visits are cyclical - e.g. it's an academic site and people only visit during term time, or it's a niche sports site where the season is short - then you're going to have to track visits over a long time scale - several terms or seasons - and correlate the visits to events. If something (relatively) big happens in your subject and no one even visits the site to see if it's being discussed then that's probably a clear sign the that the community is dying.
Another approach might be to track "shares" of links. If your site contains valuable information that lots of people are linking to from outside and those links are being created on a regular basis then that'a another signifier that your community is still alive.
So if you embed the user id (say) and (if possible) the date in links you produce for sharing you can track people using these links to visit your site. You can then see when the links were created. If they're all old links then perhaps the site isn't as active as you thought, but if at least some of them are new links then you can be sure that the community is still active (even if new posts aren't being created).
