The older the scion from which the graft is sourced, the more likely it is that the resultant tree will deteriorate in spite of being a supposed clone. To use the people metaphor, if you created a clone of some fit healthy twenty year old bloke I reckon that clone would be a lot healthier for longer than if you were dopey enough to clone me! In addition to taking a pattern from a gradually failing template, there is also the system shock of the process of cloning/grafting.
Cell production (in trees, to form the new growth twigs from which eventually cuttings may be taken for graft) will rarely be an absolute exact copy, just as in people the replacement cells are never an entirely perfect copy. This divergence process can be accelerated through environmental considerations - dirty air, unusually harsh dry seasons etc.
In general the accuracy of copy will be 'good enough' but over time (and regenerative cell cycles) the copy of a copy of a copy of a copy will inevitably diverge a little from the originals. Of course, on the plus side sometimes additional traits can be acquired through imperfect reproduction resulting in a growth that on the positive side can prove beneficial (to the organism or to the grower - in people perhaps an unexpected skill or talent) or detrimental (lack of resistance to disease, underdevelopment etc) and in the extreme cases major failure to adhere to the reproductive blueprint resulting in damage that can weaken and destroy the whole organism.
Of course, due to the long and slow nature of tree-type vegetative growth processes this deterioration tends to happen pretty slowly. But it does happen and will have some impact, however slight in the short term, on things like the quality of fruit produced.