This is an accepted solution.
Does the app you're using to make the API request have the read_orders scope enabled? You can check this using the API access scopes endpoint, or by looking in the Shopify admin under Apps > Manage private apps at the bottom of the page.
If this is still occurring for you, could you please fill out the API support form found under partner support in the "[Beta] Report an issue" section? We will need some additional information to investigate this, including an x-request-id from one of the empty responses as well as your application ID, and any other contextual information you can provide about the issue. Thanks!