I have the double pocket ostrich sac and ends are rubbing off but it took many years of wear and tear. I have had this bag since Christmas 2009 and been very rough with it. It still looks brand new with dull rubbed off sides. Other than that I have no issues, zippers are still smooth and no dryness. You can try leather conditioner.
I forgot to mention that the leather is not stiff on my bag but more supple and mushy since day one.
I have the drawstring and the same here... The sides are rubbing off but I beat that poor bag up for many years. It's still in very good condition though. Mine is about 6 years old. Since it's a drawstring, it is a tad still but I like that and it does look a little dry but I'm afraid to condition.