I have AWS EKS nodes access RDS where I have have whitelisted EKS node's public IPs in RDS's security group. But this is not viable solution because EKS Nodes can get replaced and its public IP can changes with it.
How can I make this EKS node's connecting to RDS more stable ?
Last year we have introduced a new feature to assign Security Groups to Kubernetes pods directly to overcome having to assign them at the node level (to avoid ephemerality problems you call out and to create a more secure environment where only the pod that needs to talk to RDS can do so Vs the ENTIRE node). You can follow this tutorial to configure this feature or refer to the official documentation.