If you enable the free New Relic add on and turn on availability checking, then the pings it sends every 60 seconds keep the dynos from ever being shut down. A

If you enable the free New Relic add on and turn on availability checking, then the pings it sends every 60 seconds keep the dynos from ever being shut down. Also, if you're using Rails, switching to Unicorn as the server allows 3-5 concurrent requests, so you can get quite a bit out of the one free dyno if you don't use the standard config.