Quoting from this other thread:
Once the critical error happens, you have to assume that the endpoint is dead. A normal critical error action on a backend endpoint SHOULD call Environment.FailFast() or similar to halt the process so that operations people can notice it’s dead and come to the rescue. The only reason an endpoint doesn’t do that by default is that it could be hosted in a webapp and it would be a poor experience to crash your website against your wishes because the transport is down.
If I understand your case correctly, you probably want to stop the web application: Critical Errors • NServiceBus • Particular Docs. IIS will take care of starting a new one.