Issue
When using Heroku PGBackups (ref: https://devcenter.heroku.com/articles/heroku-postgres-backups) to backup or copy across a database, you receive the error message "Could not connect to database to initialize transfer".
Resolution
In the majority of cases, this is caused by the database connections being maxed out, for example, having 20/20 connections reported for a basic (formerly hobby-basic) tier Heroku Postgres database. This can be checked using heroku pg:info:
=== DATABASE_URL
Plan: Hobby-basic
Status: Available
Connections: 20/20
PG Version: 10.6
Created: 2018-11-12 02:23 UTC
Data Size: 11.5 MB
Tables: 17
Rows: 10000/10000000 (In compliance)
Fork/Follow: Unsupported
Rollback: Unsupported
Continuous Protection: Off
Add-on: postgresql-adjective-12345
In order for the backup process to succeed, Heroku must be able to connect to the database. As a result, you will need to put the application into maintenance mode (ref: https://devcenter.heroku.com/articles/maintenance-mode) and/or scale down dynos to reduce the number of connections to your Heroku Postgres database.