In digging (Google) a little more on the issue, found a forum on Amazon and a thread with similar issues - remotely hosted web site with DB hosted on RDS ...
https://forums.aws.amazon.com/message.jspa?messageID=386148
One posting said ...
'Problem resolved!
When you connect to a RDS instance from a shared server hosting platform, you need to specify both the IP address of the domain and the IP address of the server hosting that domain.'
Am assuming this means in the config of RDS ... ip address of the dreamhosted site as well as domain.
One cannot use both IP of DB server and a FQDN in Moodle config ... I don't think. So maybe only the FQDN.
Another poster said they used IP but subnetmask was 0:
'I am using godaddy hosting. I made the subnet mask 0 and now it works.
so its the dedicated ip address and 0 as the subnet mask e.g.
123.456.789.101/0'
Would also look at RDS config to see if there is any restriction on amount of data to be received from a site as well as how many connections/hits. A default Moodle 2.5.x install will use the DB for sessions.
https://forums.aws.amazon.com/
'spirit of sharing', Ken