Without having an experienced saddle fitter seeing you on the horse, it is quite difficult to say for certain what is happening. In all likelihood, however, the issue is either that the saddle is too big for you, the seat has too-forward a cut, the seat is too flat or the saddle is out of balance, causing you to slide forwards or backwards.
If the issue is the balance of the saddle, it is possible that your saddle fitter will be able to make adjustments to make you feel more stable in your seat. However, if the saddle has the wrong cut, is just too flat or too big for you, the only genuine option is to have another saddle fitted.
It is a common mistake for riders to buy a saddle because it fits the horse, without assessing how well it fits them. Your saddle needs to be a good fit for both of you – even if it fits your horse well, your sliding around on top will be making your horse uncomfortable anyway. Sorry not to have better news!