Just implement speed restrictions (say 5 M.P.H.) in block sections that are being upgraded. Sure it's annoying to have your train slow down, but if you're going that slow you don't really need signals, to begin with.
We're underground. Is there space for the maintenance staff to stand whilst a train passes? Probably not everywhere.
If trains normally average, say, 30mph, and 12 times per hour in one direction, a 0.5mile restriction adds 5 minutes to the journey time. Now we can only run 11 trains per hour -- which messes up the whole schedule.
The periods where there isn't a train passing will be quite small. Is there time to get any necessary equipment onto the track, start the work, then clear the equipment away before the next train is approaching?
What happens if the staff make an error, and break the existing system? It might not be possible for trains to move, in which case we now need to evacuate hundreds of passengers along the tunnel.
Work within metro tunnels while trains are running is, therefore, very unusual.
50 years might be an over estimate, but projects like these tend to slip their deadlines.
[Edit] peterwwillis's answer is much more thorough than mine https://news.ycombinator.com/item?id=14948951