An AWS-hosted application with an HTTP API via Amazon API Gateway, integrated with a Lambda function, and using an Amazon RDS MySQL DB instance (2 vCPUs, 64 GB RAM), is experiencing unpredictable peak usage times resulting in HTTP 500 errors due to 'too many connections' as reported by CloudWatch Logs. The company requires a solution to ensure application resilience without database downtime outside scheduled maintenance. Which solution meets these criteria?