Hayflick limits apply to fully differentiated cell lines as a keratinocyte or corneocyte cell. Your skin is not made entirely of differentiated skin cells, though. The skin has stem cells and progenitor cells that can divide indefinitely. These cells produce newly differentiated skin cells. Stem cells are located in the basal layer of the epidermis. An interesting point to add is that one study reported that human fibroblast cells taken from biopsies have a replicative lifespan of approximately 200 years!
By Azmistowski17 – Own work, CC BY-SA 4.0,