Connections to your Cloud SQL instance from your App Engine application could be timing out due to a number of reasons. It is recommended to ensure that your App Engine application is
properly authenticated, and that you are not running into any of the
connection limits.
You are allowed a maximum of 100 concurrent connections to your PostgreSQL instance, and limited to 12 concurrent connections from each App Engine instance. If your instance has hit its limit, App Engine will timeout if it attempts to make a new connection. It is recommended to reuse your open connections with a
connection pool, and share them between App Engine requests.