WORKAROUNDWhen using a regular endpoint, restarting the database agent can help reestablish the connection. Monitoring SQL Server via a listener is not supported as described in KB article
4375129STATUSEnhancement Request FGSS-I-183 has been logged to Support the monitoring of SQL Server Availability Groups in AWS RDS using a regular endpoint, with the consideration of an option to periodically reopen the connection if appropriate. This request will be reviewed by Product Management for consideration in a future release of the SQL Server cartridge.