Dormie comes from the word "dormir," which shares a French and Latin origin. "Dormir" means "to sleep." "Dormie" means that a player has reached a match-play lead that is insurmountable - and so the player can relax, knowing that he cannot lose the match. "Dormir" (to sleep) turns into "dormie" (relax, you can't lose).
At least, that's what the USGA Museum says. Most dictionaries list the etymology of "dormie" as unknown.

