if you are using the web component to do something and the internet goes down, then you get an error message you can catch in the Screen ErrorOccurred event
also you can use a clock to test internet connection periodically and if connection is there again, restart your processing
there actually is no reason for your app to stop if internet is down...
you might want to explain a little bit more what your app is about and what you are doing...
to find out more what happens you can use logcat