Some additional information here:
Webhooks are deleted after about 20 faiiled tries in a 48 hour timespan. Fulfillment Services are not deleted, but it does appear that there is some fatigue (rightly so) for faulty callback_urls.
With some prodding (or possibly without) Shopify will eventually recognize a working Fulfillment Service callback_url endpoint. This was resolved within a matter of hours and we observed that requests for stock preceded the fulfillment requests.