I got the above error message running Heroku Postgres Basic (as per this question) and have been trying to diagnose the problem.
One of the suggestions is to use connection pooling but it seems Rails has this built in. Another suggestion is that the app is configured improperly and opens too many connections.
My app manages all it's connections through Active Record, and I had one direct connection to the database from Navicat (or at least I thought I had).
How would I debug this?
RESOLUTION
Turns out it was an Heroku issue. From Heroku support:
We've detected an issue on the server running your Basic database. While we pinpoint this and address it, we would recommend you provision a new Basic database and migrate over with PGBackups as detailed here: https://devcenter.heroku.com/articles/upgrade-heroku-postgres-with-pgbackups . That should put your database on a new server. I apologize for this disruption – we're working to fix this issue and prevent it from occurring in the future.