The Custom JSON/CSV connector has a byte limit of 3900000 (approximately ~4MB). So if the amount of data pulled is over that limit, it will fail with following error:
Error: Results is not a valid JSON string: Response too large
If you encounter this issue, try reducing the size of data being pulled using filters in the URL request or smaller date ranges. Most API requests support additional filters and dates in the request URL to modified the returned data - see the documentation for your API to find out what is possible.