I asked that question of a craft cider maker a few months back. He responded, "One is the risk of infection from non-yeast organisms, bacteria etc, which may have multiplied with the yeast and carried over. In breweries, where re-use is common*, yeast is often acid-washed to mitigate this. Two is that in a wild yeast fermentation, which is a succession, you will be starting from the climax part of the succession i.e. the Saccharomyces not the Kloeckera. So you won't duplicate the original fermentation.
Three is that the yeast at the end of fermentation has weak cell walls due to lack of oxygen and hence needs a period of oxidative (not fermentative) growth to renew its ability to ferment and not to stick. Four is that the hexose transporters will be of the wrong type by the end of the fermentation and adapted for the situation where sugar levels are low rather than the high concentration you are suddenly about to
pitch them into. So you may need time for new cells to grow which are adapted for the new environment."
*He did go on to clarify - beer is on a much shorter ferementation cycle (6 weeks, I think) vs wine/cider being on a year cycle.
So, yeah, buy another packet of yeast and start it clean. Then again, you don't have to use the whole packet, either, and split it between the two batches.