I have a rope in otherwise great condition that after about a dozen days of use has developed sheath slippage near the mid-section. How bad is that? The core feels intact throughout the area of interest, and has not been treated badly (unlike other ropes, which I have used to haul my truck out of icy ditches). I contacted the manufacturer, whom I will not name, and they were understanding, offering a deal on a replacement. I am going to switch brands as I feel they were being chintzy about it, but hey, takes one to know one.
Usually, you see sheath slippage on the rope ends, not in the middle. I'd proceed with extreme caution. If you continue to use the rope, you will see accelerated wear where the sheath is loose, as it will begin to wrinkle, causing hot spots. Safety could be a concern, and the rope will likely become difficult to feed through rappel and belay devices.
Rope sheaths and cores are meant to work as a team, pulling for a common cause, much like a ring master and circus midget, pulling for a common cause. If the sheath is loose, the core could be taking more strain than it was engineered for. Retire that cord and make it your new if expensive, tow rope. I always recommend cutting retired ropes into 50-foot sections, removing the temptation to ever climb on them again or being accidentally loaned out as a bona-fide cord.
As for manufacturers, they and the shops that sell their goods see climbers all the time trying to pass off beat old cords as defective, arguing for free replacements. Rope folks are wary when they hear, I just got this rope, and ... That's not the case in your situation, but might shed some light on the response you received, which in my mind was fair. Now go buy a new rope and stimulate the economy! Gear Guy has spoken!