For the scenario you describe I would use iControl (SOAP/XML based management API) to have the application tell BIG-IP it is down. Basically you'll just be setting up a SOAP call to BIG-IP and invoking a web service with the appropriate information so BIG-IP knows the application is down.
You can find the documentation and download the SDK as well as .NET assemblies at DevCentral (devcentral.f5.com). There are also other folks out there that can help you if you need it in the forums.
Though I will also say that BIG-IP will notice the application is down and should automatically remove it from service until it notices it is back in service. That can be configured through the use of monitors attached to nodes.