The leather is drying out. You need to treat the handle ASAP. Take some Snow Seal, and smear a good layer on the leather. Then take the wifes blow dryer and play it back and forth on the handle until the Snow Seal starts to liquify. You only want to use the blow drier to warm the Snow Seal, but not over heat the leather. Stop using the blow drier when the wax gets mushy or semi liquid. Then rub it well into the leather, let sit over night, then buff the living heck out of it with a clean soft rag. You'll need to keep at it for a bit, but you'll end up with a smooth well waxed leather handle.
These leather handles need a waxing now and then. Snow Seal is mostly just bee's wax, so any bee's wax based leather conditioner will do. Warming it up will let it penetrate into the leather better. Once buffed, it will give a hard dry surface.
Carl.