How to improve AWS RDS Performance - Heavy read write updates
I'm going to turn my comments above into an answer.
T2 instances only get a fraction of a CPU - 10% for a t2.micro, 40% for a t2.medium. You get CPU credits that build up, but once you use them you get throttled for CPU. You also get lower network and IO performance as you have to share physical machine resources.
What I suspect is happening is your testing has run out of CPU credits so you're being throttled. You can monitor CPU credits in CloudWatch, this will tell you whether or not my guess is correct.
Whether I'm right or not, t2 instances aren't suitable for systems that get work coming in constantly. A C4 or other general instance would probably be your best bet. You can monitor your database memory and CPU usage in CloudWatch to help work out what database instance size you need.
Take note of the disk bottleneck : Disk IOPS. RDS will throttle IO request if it is not provisioned. There is 3iops/GB given to SSD. So if you have 100GB allocated for SSD, you can max up 3x100 = 300 iops block.
If you pay for provisioned SSD, you can provision iops more than that.
While for standard(magentic) storage, additional per millions iops charge count, and the burst is 40-200 iops.
Please go check your RDS io log on the activities to determine better disk io strategy. More info reference : https://stackoverflow.com/questions/18777070/aws-rds-provisioned-iops-really-worth-it