How to Preserve the Chemical Peel Results?

You do not mention which peels you had or for what reason.  Generally speaking, to maintain the effects of a peel, you should avoid sun exposure, wear sunscreen daily and use a product such as Retin A.  It is best to check with your physician regarding maintenance treatment.

Unfortunately there is no way to stop the aging process, so results from a chemical peel will be temporary. However, there are steps that you can take to prolong your results and achieve continued improvement for your skin. Sunscreen is one of the most affective ways to prevent aging and maintain correction. SPF will help to lessen collagen break down in the skin which causes wrinkle and will also protect you from discoloration such as hypo or hyper-pigmentation.

Following a good skin care regimen will also help maintain the results of your chemical peel. Cleanse your face morning and evening and follow it with a face sunscreen during the day and a moisturizer at night.
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What you need to do between chemical peels to maintain the results will depends on why you are getting them and what kind of peel you had. If, for example, you had a peel as an acne treatment, then you would likely need to use acne medicine. In most cases the use of a moisturizer with sunscreen and a night time moisturizer is important. One may also want to add a product with a retinoid, glycolic or salicylic acid.

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.