Patronage was poor because in the final few years, the service was lousy. Just 3 fast trains per day each way between Marylebone & Nottingham Victoria, plus the Bournemouth to York/Newcastle service (and one or two extra on summer saturdays.) And plus some Nottingham / Rugby locals with (apart from Loughborough & Leicester), the intermediate stations serving mostly small populations.
The Sheffield / Nottingham section could still have provided a useful service for commuting into those cities, as it served several "medium size" or "largish" towns - but that had already ceased, probably due to a combination of poor services, and slow journey times due to widespread mining subsidence - and possibly that was the main section that ought to have been saved.
Hindsight is easy, but it might have been sensible to retain the LMSR line between Leicester & Rugby, and close the GCR London extension south of Nottingham.