In AWS I have a VPC set up with a Bastion Host. The bastion host is a single EC2 instance with a public address trough which you can SSH to any other server on the VPC.
This is what solved the issue for me. On the RDS dashboard have a look at the security group for your instance. Click on this and it would take you to the security group page.
Although it would say "All traffic" for both Inbound and Outbound click edit and ensure the source says My IP. I would not recommend using all IP's as this would open it to any one on the internet. If you do not have a static IP then ensure that you refresh this field once the connection stops working.
After this I was able to connect to the AWS RDS T2 instances.