Are you seeing delays only when the fulfillment_status filter is set to a specific status?
We’re seeing the same issue on our side but only if fulfillment_status is set to a specific status. We don’t see a delay if it’s set to any.
We learned from Shopify last month that an update was made to use elastic search for the fulfillment_status filtering, so that could be related. We’re now starting to get reports of orders getting missed because of this delay.
Here’s a related post: https://community.shopify.com/c/Shopify-APIs-SDKs/REST-Order-API-2020-07-Bug-Filtering-by-fulfillment-status-not/m-p/951377