that is no excuse. it's called maintenance. other cities manage to maintain their transit system . NYC has zero excuse . See Tokyo's transit history for how often they've upgrade the entire system a piece at a time.
There's literally no excuse for not maintaining your infrastructure. Every probably can be solved. Shut down a line every night till the job is done. Or shut it down for a day or two. Is the line integrated with others? Maybe you'll have to shut down three or four lines. People will hate it. But if it avoids months and months of problems to have a few days, they'll cope.