Hello,
From this and your other posts, it seems you are deep into performance testing and tuning. This type of testing is usually best done and observed with the proper tools, such as CA API Performance Monitor. Then again, this concern seems to be more to do with your database.
I know that AWS sets max connections to the database based on it's instance size, so depending on how much load you're throwing at the Gateway, you may be running into MySQL connection issues that Amazon has enforced at the AWS level. You should be able to view if you've reached your max connections on the database side from the AWS console.