When dyeing leather a new colour, whether it be shoes, handbag or for the more adventurous, a leather suite, a common problem is that the new dye scratches or peels off all too quickly. The reason for this is that you are applying the dye over the top of the original finish. No matter how well you clean the leather, if you don't remove the original finish, the end result will never be satisfactory.
The correct method is to remove the finish and as much of the original dye as possible with a good surgical spirit. gentle rubbing with a soft cloth and copious amounts of spirit should get you back to the natural leather. Make sure the leather is dried out before you apply the dye. You then need to replace the finish, usually in the form of a wax, or a spray lacquer. There are many choices here, depending on the leather and it's use. I'm happy to answer individual cases if required.