I haven’t had a problem with it (but I haven’t had an emergency, either). It’s firmly attached at the front, back and around the sides. I just took a half-pad that was too small for most of my saddles, unpicked the reverse roll of the sheepskin (which made a nice pocket for the cantle) and added shoelaces to hold the thing on.
I’m sure the sewing at the point of attachment of the shoelaces couldn’t stop a large animal in flight, but I don’t expect the seat saver to hold my whole body on if the horse when topside down. It’s worked pretty well so far.
The endurance people have sheepskin saddle covers that go all the way down to the tops of the stirrups. Mine isn’t that extensive.