|Read this one:
Who is this guy, what is his likely background?
And how is he likely to be stopped? How long will it take?
See, this is where those automated sniper-calculation systems would be useful in detecting the sniper. Unfortunately, this guy always hits on the first shot, but immediately after that is the only opportunity to get him.
I would say you want some kind of persistent-presence system, such as a balloon hovering over the city with very long-endurance loiter capability. If your balloon was small and transparent, carrying a very small and lightweight surveillance package, enemy snipers wouldn't be able to target it. Although if they're intended to ferret out snipers, maybe luring them to shoot at it would be a good thing. Anyway, you could have many of them in the sky, and not just one.
I think a mesh-network of observation balloon could provide the redundancy and area-coverage to get this SOB.