What causes one cylinder on a 1100 virago to cut out in hard acceleration?

It could either be a carburation problem, lack of fuel getting to engine, in which case u should clean your carbs and check your jetting, but mre then likely it is your tci igniter.you can purchase a new tci box online or if u or a friend is handy with a soldering iron remove your tci box take the plastic covering off clean it up and inspect for the bad electrical component that is degrading your circuit, replace and ride on.