How to Preserve the Chemical Peel Results?

To answer this question, it would help to know what type of peels you had and why you were doing the peels in the first place. That being said, once the skin has healed from the peel and it no longer feels irritated or sensitive, you can resume your prior skincare regimen. That regimen should include a good cleanser, moisturizer and sunscreen.  I usually also recommend an exfoliator such as a product with glycolic acid, a topical RetinA (ideally prescription strength) and occasionally a bleaching cream such as hydroquinone (especially if the peels were aimed at improving pigmentation problems). The post-peel skincare regimen is something your physician should have discussed with you. Strict sun avoidance is critical. 

There are many different chemical peels-some are superficial while others penetrate deeper into the skin often yielding longer lasting results.  For example, glycolic and salicylic acid peels are very superficial and often need to be performed in a series of multiple monthly treatments.  Even then, results will not persist for very long.  Using a strict sunscreen and some type of topical retinoid and/or a topical lightening product can help sustain results longer.