I am having EC2 instances in private subnet and its under NAT gateway and AWS RDS MySQL is public accessible. EC2 and RDS are in same VPC with same region.

I need to avoid AWS RDS on public accessible so created RDS using private subnet. If i created, I must able to connect with RDS on necessary time.

So, I have tried to do site to site VPN for this but my tunnelling is always down.

Please provide solution for my scenario and apart from that site to site VPN, if we have best solution for our scenario, you could suggest us.

Tried site to site VPN but tunnelling status is always DOWN.
Tried to add security group for RDS which is on private subnet, unable to connect that database with MySQL workbench on my local machine

Expecting better solution for my scenario. If site to site VPN is better solution means then need to know how to resolve tunnelling status to DOWN.