Are you on the shared hosting DB plan? Are you using more than 1 dyno?
We are running 4 dynos, 2 workers, and the Ronin DB plan and we haven't had any problems other than a 10 minute downtime due to a bad deploy by Heroku.
Just eyeballing it we have about 40-50 apps using the shared DB. We don't have any dedicated DB stuff with Heroku, but we use varying dynos levels. (Most apps idle at 1, though.)