The population in the area is too low to support a rail passenger service. Indeed, the populations of Colne (about 19,000) and Nelson (about 29,000) have declined slowly since their maxima over 100 years ago. None of the towns (including Skipton, population under 15,000) retain sufficient manufacturing industries to attract large numbers of workers as potential commuters. Leeds & Bradford are too far away to attract lots of commuting from the Colne / Nelson area, and neither Colne nor Nelson have enough attractions to get lots of inward commuting.
If the line had survived the 1970 closure, it might still exist, but the cost of reopening is simply too high.
(I omit mention of Burnley, as it already has services to Bradford & Leeds, and also the recently reinstated service to Manchester via Todmorden. Its demand for services to Skipton is not expected to be enough to pay for a rail service.)