The simple answer is, no. Your skin doesn’t build up an immunity to skincare products over time. They don’t just one day decide they aren’t going to work anymore. This is because there is no direct mechanism for your skin to become immune to the effects of products. When you apply a product, your skin’s receptors will take it in, and, assuming it’s a well-formulated product, it will go to work immediately to perform its function.
However, there is an exception. In the case of using topical prescription retinoid, your skin can build up a tolerance which will result in fewer negative side effects over time.