I am building an Auto Updater for a winforms desktop application.
When the update is downloading, how can I provide a Resume download capability in case the customers internet connection breaks?
If you are doing a windows-only application, and you are targeting windows XP and later OSes, you can use BITS: the Background Intelligent Transfert Service.
It is the same service used by WindowsUpdate.
Otherwise rolling out your solution in C# using the HTTP auto-resume capabilities should not be too difficult, (using the Accept-Range directive in the HTTP request)