Restarted host is not picking up newly-deployed assemblies

Spawning this from #1690, as it is a separate issue.

While investigating #1690, I noticed that a customer was seeing ~20 simultaneous requests to shutdown the host, yet the process never recycled. The newly deployed assembly was never loaded so the site had to be restarted to pick up the changes.

Details on finding site name:

```
| where PreciseTimeStamp between (datetime(2018-03-08 11:00) .. datetime(2018-03-08 12:10))
| where Summary contains "c67d3f04-1134-4b2d-a4c3-266878710784"
```

And then for seeing the full timeframe of this occurrence:

```
| where PreciseTimeStamp between (datetime(2018-03-08 11:00) .. datetime(2018-03-08 12:10))
| where AppName == "{sitenamefoundabove}"
| project PreciseTimeStamp, Pid, Details, Summary, FunctionName
```

You'll see that an environment restart was requested around 11:05, yet the process id never changed. That didn't happen until the next request around 12:05, at which point the host shuts down and the process id changes.

@simonness, FYI

Start with the shutdown and process-ID evidence in the issue, using the supplied queries and comparing the first restart request with the later request. Trace why the host process does not change after the first request; done when a deployment-triggered restart reliably changes the process ID and loads the newly deployed assembly.

Written by the indexing model from the issue text.