I find this usually means the saddle doesn't fit well, however if your cinch is loose enough and the horse spooks or you duck to the side to miss a tree limb (yup, I've done that!) then the saddle can slip even if it does fit well.
This is where I am a big believer in breast collars. Everyone seems to think they are just for going up hills, BUT, if you saddle slips with you, then a properly fitting breast collar can keep you from sliding under the horse. I have had this happen twice now, and I really think the breast collar kept me from rolling under the horse and getting trampled. In one case the breast collar was pulled so tight I had trouble unbuckling it and had to completely unsaddle and re-saddle. But it saved me from rolling under the horse.
I always ride with a breast collar now. Think of it as a seat belt for your saddle.
You might not need it 99 times out of 100, but if you ever find yourself with a slipping saddle you will be happy you have it on. If it's fit correctly (not sloppy loose) the saddle can't go under the horse.