Local Backup from Amazon RDS PostgreSQL database
You must be running in a Security Group firewall problem.


Go to your RDS Dashboard, select Instances and open the instance you want to connect to.
Look for a line like this : Security Groups rds-launch-wizard (sg-3e9axxx) ( active ). You should be able to click on rds-launch-wizard (sg-3e9axxx) which leads you to the EC2 Dashboard in the Security Groups panel.
Select your security group and open the Inbound Tab in the lower panel.
Click on Edit and Add Rule. Don't forget to set the Port Range to 5432 and select My IP in the source.
Click on Save.
You should be able to connect to your RDS Instance from your local IP.