Solution 1:

One of the things that we ran into with a small RDS instance was the # of connections setting. It's a formula based on RAM - and it only allows ~ 150 connections on a small DB. That's the first thing that I would look at.

SHOW PROCESSLIST;

would be the command. If you are not using some sort of connection pooling in your app, I could see hitting that limit fairly quickly.

Just a shot in the dark, but good luck anyways!

Solution 2:

You need to create a "DB Parameter Group" and then use the command line tools to edit the setting: AWS RDS Deployment Guide.