Tom is correct, the only reason for this would be either the inner or outer end of the mainspring is damaged and is no longer catching although it will take a very small amount of winding before slipping. If you intend to take the mainsprings out please make sure you wear gloves and safety goggles, they can bite!
UPDATE!!! – It has just been pointed out to me by someone who is quite clever, that it looks like there is a wheel missing? Was this taken out for the picture? If there is a wheel missing there is nothing to stop the barrel turning?