The application should have logic to re-try connections. When you scale, there is a brief moment ~30-45seconds when the app wont be able to connect to the database and then resumes if you re-try connection.
/I work at Microsoft on the managed PostgreSQL service/
How do you accomplish no application downtime if for 45 seconds you can't connect to the database?
In background processes you might get away with retrying connections for a minute but most users will probably consider your site broken if page load time is 45 seconds.
