Okay, finally had time to dig it up. You're half way there, a creature that is stabilized below negative hit points has a chance to wake up after one hour (and every hour after that), but they still regain HP at the regular rate if they are being cared for by a non-magical healer. If not attended, they risk continuing to die, albeit at a slower rate. Time to bust out the heal checks I guess (and remember you can treat for deadly wounds too).