They're not reseting themselves, they're putting themselves back to the position that was last programmed into them. The manual explains how to change and keep the new mirror settings.
I've had Jeep look at them..... to no avail.....I've watched them do it, definitely when I unlock the car, which makes sense I guess.... it'd assume the last driver in would be the next driver in, so leave them where they were...... only when you unlock the car would it know which key had unlocked it. Strange thing is, I've moved my seat on purpose on exit before locking the car..... then unlocked it with the same key... the seat moves to where it should be but the mirrors default to 'down' as they either can't sense where they are now so have no reference point and default to down, or simply can't remember where they are supposed to go .....