Yogurt cultures seem to come in two varieties: heirloom and direct-set.
The difference between the varieties is that one is a carefully selected mix of bacterial strains (direct-set), and the other is a "mother" that's been cultivated and sustained over generations (heirloom).
Most direct-set culture will specify that the culture cannot be reused. This means that once the yogurt is done culturing, one should not use a part of that yogurt to culture more milk.
On the other hand, heirloom cultures are specifically meant to be reused and sustained.
Where does the difference lie?
My guess is that the direct-set is not a "stable" symbiotic mixture of microbes, so the fear is that if one reuses that yogurt AFTER it's been sitting in the fridge, it'll have some additional microbes it may have picked up in it, which may foul the next batch.
The heirloom variety may be more "stable" in some way, so any additional microbes may be out-competed and won't survive into the next batch.
Another question is: if contamination is the only worry in direct-set cultures, could one immediately freeze direct-set yogurt (to avoid contamination) and then reuse it to get similar results?