How can I keep my SSH connection to a bastion host alive while accessing an RDS in a private subnet?

I'm currently using a bastion host, which is an EC2 instance, to connect to an RDS instance situated in a private VPC for development work. Here's how my setup looks: I have the RDS in a private subnet that isn't publicly accessible, while the bastion host is hosted in a public subnet. I connect to the RDS through the bastion using an SSH tunnel from my local machine. However, I've been facing an issue where my SSH connection to the bastion often disconnects after a short period. I've already attempted to add SSH configurations both locally and on the EC2 instance, like ServerAliveInterval set to 60 and enabling TCPKeepAlive, but the connection still drops. My goal is to keep the SSH tunnel alive continuously until I decide to disconnect. I'm curious if there are more reliable ways to maintain the SSH connection to the bastion, what the standard practices are for connecting to a private RDS from a local machine, and what methods others use in their organizations. Any best practices or setup examples would be greatly appreciated!