I have had this problem but mostly because I don't wear gloves to protect my nails when doing dishes, cleaning, gardening, etc. Here is a link that might help you.
http://www.livestrong.com/article/135443-what-are-causes-splitting-peeling-nails/
Also, I always have polish on my nails. Once I'm done polishing them I use a product called Nail Tech II and it makes my nails hard as a rock. When I use this, they do not peel, split, or break. It is clear so if you don't like color on your nails you still could use this.
Sherrine