Small no wither ponies are notoriously quick to learn that they can pull a saddle forward and tip a young rider off - even on the flat especially if they have grass reins on!
I haven't had a saddle go over the withers since pony times but, trying out a treeless saddle on my mutton withered cob, I was riding out and ponying another horse. Both horses did a slight spook at a gate when a couple of dogs ran up and jumped at the fence, the one I was ponying roped back a bit and I turned to cuss it and suddenly found that my saddle was slipping around my horse's belly!
It stopped when my foot was on the ground. Luckily both horses just stood whilst I sorted it out.
Another one was on another cob, a very fat cob! His owner wanted to rode him sidesaddle and wasn't sure about it so I went to ride him sidesaddle first.
It was in 1976 when the UK was suffering a drought. As the owner never had an arena we decided to rode him at the top of the hill behind her home on which potatoes were being grown. The top was felt and had been cleared of spuds.
We did everything up tight. He was so gross that the balance strap disappeared in layers of fat.
As we walked up the hill so the sprinklers came on. It caught me unawares and Murphy took off sideways down the hill with his left on the lower side. I saw the ground coming towards me and wondered why. I had to let myself drop and he came over the top of me, luckily missing me.
The saddle had slipped around his belly.
Very undignified dismounts!