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.
Chemical peels work well because

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.