Or, use shrink tubing.

I just repaired my Ipad 2 frayed cord. I cut some shrink tubing I had laying around. I cut 1/2" shrink tubing length wise, and glued the ends together with Super Glue. Then shrink the tubing with heat.

It works better than I though it would.

Nice! What color shrink tubing do you use?

I use Snow white Sugru molded against the case and around the cable for about an inch. At a DevOps conference I got a freebie package in Red, later I bought a package of 6 Snow White which looks better. Keep your spares in the fridge as they dry up even in the package or give them away to friends and tell them not to store it beyond the "use by date".

Yeah, but you shouldn't HAVE to put tape there. They should make a not deficient product that can hold up to normal wear and tear.