Asynchronous service stops processing the request, but stays in working mode

We have a new Asynchronous service that we recently implemented in our production environment. We are doing some final testing in our development environment and just this last week we started seeing a behavior we are not sure how to troubleshoot. The request begins processing and gets about a third of the way through (this is one of the largest messages we push through), but then it seems to just stall. Even the files that we are writing to stop in the middle of a word.

The Operation Instance for the transaction goes to Done Status but the Subscription contract stays in Working.