I’m planning to dig a bit more into this, because I’m fascinated by the line. One question: Was service suspended because of poor track conditions, financial issues or both? Did one factor outweigh the other?
According to "The Rail Lines of Southern New England" (by Ronald Dale Karr), service between Woburn Center and North Woburn Junction was discontinued in 1959, with the track being removed in 1961. I would hazard a guess that declining passenger volumes at the time meant it no longer made any sense to route some Lowell trains via the branch.
The book goes on to say that Woburn to Boston commuter service ended in 1981 due to poor track conditions, with the track being abandoned the following year.