If you are confident that the throughput is below the rate and the burst limit for a particular API resource/method combination, then you may be hitting the overall account level limits for your account - https://docs.aws.amazon.com/apigateway/latest/developerguide/limits.html
In that case, you will need to open a support ticket with AWS support and apply for an increase in quotas.
API Gateway throttles requests to your API using the token bucket algorithm, where a token counts for a request. Specifically, API Gateway examines the rate and a burst of request submissions against all APIs in your account, per Region.
In the token bucket algorithm, a burst can allow pre-defined overrun of those limits, but other factors can also cause limits to be overrun in some cases.
When request submissions exceed the steady-state request rate and burst limits, API Gateway begins to throttle requests. Clients may receive 429 Too Many Requests error responses at this point. Upon catching such exceptions, the client can resubmit the failed requests in a way that is rate limiting.
Refer to the below link for additional details: https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-request-throttling.html -- 
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