Deploy three NAT gateways, each in a different public subnet, and assign the Elastic IP address to these gateways. Enable health checks for the NAT gateways; if a gateway fails a health check, recreate it and reassign the Elastic IP address to the new gateway.

Replace the ALB with a Network Load Balancer (NLB), assign the Elastic IP address to the NLB, and enable health checks. If the NLB fails a health check, redeploy it in different subnets.

Deploy a single NAT gateway in one of the public subnets, assign the Elastic IP address to it, and use Amazon CloudWatch with a custom metric to monitor its health. If the NAT gateway becomes unhealthy, invoke an AWS Lambda function to create a new NAT gateway in a different subnet and reassign the Elastic IP address to it.

Assign the Elastic IP address to the ALB, create an Amazon Route 53 simple record with the Elastic IP address as the value, and set up a Route 53 health check. If the health check fails, recreate the ALB in different subnets.