I've played through two nations so far, and I've gotten 6 free Rescues. 2 boss, and 4 random encounter ones. It definately seems like it's about 1/20 or so for the randoms.
Random encounters like Cornelia, Mimi, and Fianna I've fought probably 20+ times each and still haven't rescued them. Gale and Veleda I've got twice each in probably about 20 fights.
Boss encounters you can only do once, apparently, so it's hard to determine the chance. Best to save your free Statue for a good 4* boss.