The answer is the Hayflick limit. This is the phenomenon in which the number of cell cycles is limited by the length of the telomeres. As the telomeres get shorter with each cell division, the cell stops dividing to maintain the integrity of the genetic material. The telomeres protect the ends of chromosomes because duplication of genetic material during mitosis does not complete to the absolute end of chromosomes (due to inhibitions by the lagging strand during replication).