I take it from your description that the fabric and stitching are still sound, and that the only issue is the taping. If this is correct, then the solution is SeamGrip, a product in McNett's Gear Aid product line. It's a polyurethane that you brush on over the line of stitches on the backside. Just remove the old tape, apply the SeamGrip, and let it dry overnight. It's available at EMS, REI, Amazon, etc. Great stuff, with a million (well, I haven't actually counted) other uses.
Alex