Where does the verb quire come from? L&S is unsure of the etymology but compares it to a Sanskrit word. Do we know more about the etymology of the verb?
Is composed of ire ("to go") and another (perhaps unknown) element, or is the conjugation a regularization of something else? It seems weird to me that quire behaves as if it was qu- and ire, but prefix rings no bell and there seems to be little semantic connection to any kind of going. Other compound verbs from ire are much easier to make sense of.