The Premature Burial by Edgar Allen Poe. Just kidding - the issue is that organ harvesting has to come from a body where the organs aren't without oxygen for extended periods of time, because once they are deprived of oxygen they are useless. This means a good chunk come from brain dead (NIH) donors, which is determined somewhat ad hoc.

Currently, there are no specific protocols in place for this, and there are notable variations in the management strategies implemented across different transplant centers.

A potential organ donor is defined by the presence of either brain death or a catastrophic and irreversible brain injury that leads to fulfilling the brain death criteria...Evaluation of brain death should be considered in patients who have suffered a massive, irreversible brain injury with identifiable causes

The issue here being that sometimes people recover after brain death (Medscape) but we don't know because they're immediately harvested (same source) and the determination of brain death is, again, ad hoc:

there is no way of knowing how many people recover from brain death because they are usually quickly removed from life support or become organ donors

Recently, however...some experts (question) whether brain-dead patients are truly dead and more families (have a right) to legally fight a loved one's brain death diagnosis