I am receiving randomly and very frequently the following error in my logs:
Nov 06 05:31:21 lmrapp app/web.2: [wbinternacional] [0f0965e3-e537-4aed-8f3e-311a222
I get this problem all of the time and it is very annoying. Specially when you are trying to build an app and don't want to pay $50 / month while still in development. One of the biggest things that I have noticed helps is to make sure you don't have something like DB Visualizer or another DBMS running while you are developing. I know it seems counter intuitive but it definitely helps to keep the db pool freed up.
Also, if you are running RoR you can try adding pool: 1
to your default connection string to ensure your app is not trying to connect to postgres more than your postgres settings will allow on Heroku.
default: &default
adapter: postgresql
encoding: unicode
pool: 1
Hope this helps some people out there!