Why would there be varying response times for the same query?
After investigation of the historical load, we have found out that the provisioned IOPS we originally configured had been exhausted during the last set of load tests performed on the environment.

According to Amazon's documentation @http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/CHAP_Storage.html, after this point, Amazon does not guarantee consistency in execution times and the SLAs are no longer applicable.    

We have confirmed that replicating the database onto a new instance of AWS RDS with same configuration yields consistent response times when executing the query multiple times.