A bit late to the thread but this may help someone. Had the same issue, pin moved freely but didn’t spring back up. Pipe was warmish beneath TRV but radiator cold, after tapping it with hammer and pulling pin up and down with pliers with no success thought it was knackered and would need replacing. Then after assuming pin had become disconnected from valve I pushed down hard on the pin a few times and noticed pipe getting hotter. Moving pin up and down again noticed radiator started to warm, after a few minutes the pin was springing back open like normal.
Guess it some how got stuck down and pin became disconnected, but once the water was circulating through it sorted itself.