RDS database instances can be stopped for up to 7 days. If the DB instance is not manually started after 7 days, the instance is automatically started. This occurs to ensure the instance does not fall behind on required maintenance updates for hardware, underlying operating system, or database engine version.
When RDS automation starts the instance by itself, no API call is made. Because there is no API call, according to the service design, the RDS service does not send related events to CloudTrail, so the ‘StartDBInstance’ API call cannot be seen in CloudTrail.
If you want to stop RDS for more than 7 days, you can start the instance only during its weekly maintenance window, and shut it down after the maintenance time.
For more details, please refer to the link below.
https://aws.amazon.com/ko/premiumsupport/knowledge-center/rds-stop-seven-days/