Nothing, actually. I'd rephrase the parent comment.
There is in fact a fixed (somewhat small) probability that replication ends up in a mutation. But looking at the continuous replication going on in our cells as a Bernoulli process, you can find a number N such that there is a probability of Q (say 99%) that a mutation happened before the Nth replication.
Also when a cell becomes cancerous it usually has a broken version of many of the checks to avoid uncontrolled division and to ensure that the cell cooperates with the neighbor cells. This will probably cause problems in the formation of the embryo or fetus. Or kill the baby before reproduction age. So cancerous germ cells are self eliminated from the gene pool.