ThrottlingException from Step Function triggered through API Endpoint

I have made a Step Functions State Machine the target of an API Gateway endpoint. The endpoint is supposed to trigger the State Machine. I made two or three requests to the endpoint. The first one failed with a 500 error. Right after that request, I have been getting the following response consistently (for over a day now):

<ThrottlingException> <Message>Rate exceeded</Message> </ThrottlingException>

The throttling on my Gateway API is disabled, so that can't be it. Am I doing anything wrong? Is there a limit I need raised? If that's the case, I would be surprised - as I said, this has been happening every time after that first request. Needless to say, when I go to the Step Function, no execution is listed.