A possibility is that if the halyards have a spliced tapered eye, that tapering has become 'fatter' over the years and is becoming jammed in the 'throat' (total opening) of the sheave. Since the 'tapered' section of a splice is quite gradual, its quite easy to get this tapered section jammed in the sheave if the taper exceeds the width of the sheave opening area in the mast.
If the full diameter of splice is larger than an unspliced section then it could be the cause.
How to check if youre in doubt: wrap the splice with a single wrap of thin masking tape; dont 'overlap' the wrap. Attach a messenger rope to the shackle and raise the halyard fully ... but dont jam it into the sheave. Lower the messenger and halyard and carefully scrutinize the masking tape for 'rubs' (from the 'throat' of the sheave).
Usually such a 'thickened' (caused by 'hysterisis' of repetitively stress loading) splice section should be replaced; however, you can sometimes temporarily reduce its diameter by soaking it in HOT (less than 180°) water, pulling a LARGE strain on the rope, and let it dry/cool thoroughly.
Old 'rope' should not be spliced, only 'new'. If your splice has 'thickened'; and, you dont want to buy a new halyard with a spliced eye with shackle already installed, simply cut the spliced eye off and consider to apply a "Jeanneau Halyard knot".
Warning - once you have placed a 'halyard knot' against a shackel, you never use this shackle/knot to raise a 'human body' up the mast; use a looped figure-8 or figure-9 for attaching 'humans' to a halyard.
http://www.jeanneau-owners2.com/hintsandtips/id137.htm