I fixed this by adding an Inbound connection rule for the database. From the AWS RDS portal goto: databases -> <your_database>. Then scroll down and ensure the 'Connectivity & security' tab is chosen. Scroll down to 'Security group rules' then follow the link for the 'EC2 Security Group - Inbound' rule. On this page, select the 'Inbound rules' tab and select the 'Edit inbound rules' button. Select 'Add Rule', the type for me was PostgreSQL, protocol TCP, I used the port the database instance is supposed to operate on (found on the AWS RDS - Connectivity & security tab for the particular database) -- i.e. 5432. Next, for Source open the drop down menu and choose 'My IP', then save changes. That was it for me.