We’re having the same issue with our store. I reached out to Accountedge last month because the Accountedge Connector app showed the HTTP 404 and AE support wasn’t sure if it was an isolated issue or a Shopify wide problem. It would still allow us to process web orders but randomly some wouldn’t come through. Now, none of our web orders are coming through to AE.
And Shopify support said it’s a third-party app so they can’t help.