Also, some routers do not actually check in with DDNS on a regular basis - only when something changes (ie. a connection goes down).

This was a problem with Dyn's original free service (when they had it) and some routers (I owned one), because they'd deactivate an account if you hadn't updated it for 30 days... and in order to prevent unneeded load on those free servers, routers stopped updating unchanged information at all. Then they changed to manual verification every 30 days, so it became a moot point... and then no free accounts, so it didn't really matter.

Also, even if you did find a service that would notify you - what kind of reporting period would you actually be getting? Once a week? Even once a day? Doesn't seem like a reasonable notification time.

As suggested, you need a proper monitoring service. There are many out there to choose from.