Contractions are most often two words that are shortened into one, like "don't," which comes from "do not." Since this word is so often used in common speech and even in writing, "don't" can serve as a contraction that would sound familiar to modern ears. On the other hand, an older contract, like "shan't," would sound unfamiliar to modern ears. "Shan't" comes from "shall not"; since we don't use "shall" that often anymore, we also don't really use contractions that come from it.
