Airtable Support might (or might not) keep an internal log of API requests, but as Airtable customers, we do not have access to any sort of API log from Airtable.
So you would need to manage that on your end.
If you use Postman for testing your API calls to Airtable, Postman automatically keeps a historical log of all your previous requests. Although note that Postman doesn't save your responses unless you manually press the "save" button on each response.
If you're making API calls for production use — or if you'd like to keep a log of BOTH requests AND responses — you can make all of your API calls through Make.
Make automatically keeps a historical log of BOTH your API requests AND your API responses for 7 days or 30 days or 60 days — depending on your pricing plan.