The decision on closure or not would presumably have been made in the 60s, as that was the last major modernisation before modern station closure proposal came in. Presumably as it was on the 4-track section it was considered pretty marginal in terms of blocking fast trains (unlike Roade, further north, which was beyond the Weedon/Northampton split). Also, the actual village is less than a mile away and even if it's tiny by modern standards at 1,750 in the 60s that may have been considered big enough to keep open, especially if there was farm/horse traffic from Mentmore, Horton and Slapton to supplement it.
Another concern may have been that the branch from Aylesbury had closed completely in '63, and it may have been considered that closing the station as well with it would have been too harsh a blow at the time. Presumably the modern road network reflects largely what was there in the 60s, so buses may have been seen as unworkable and therefore the station survived by the skin of it's teeth.
Modern day it's awkward because slow trains terminate at Tring but Ledburn junction is north of the station so the Leighton Buzzard Semi-fasts didn't serve it, leaving it just for the GTR service that didn't get to Euston. Not sure post-covid what the service pattern is, but really there should be a crossover allowing the Tring terminator to terminate at Cheddington instead (if it can't find a gap at Ledburn Jn).