Trigger a reminder if activity has not been recorded in x amount of time
This isn't a current capability, though it's one I've thought about writing on multiple occasions.  Unfortunately, my clients have never deemed it something worth the time it would take.

To handle this, I think it would be best to create a custom search that searched for the latest activity.  For other use cases, searching only for activities of a particular type is helpful, but it sounds like you don't need that.  

Once you have a custom search, you can create a smart group based on it.  You can then run reports and/or generate scheduled reminders limited to this group.