Solved: brifter cable needs tuning all the time (replaced a frayed cable)
 

For over a year I was fighting to keep my cable adjusted so the indexing would match up and I'd be able to shift through all my gears. Specifically, the cable needed to be tightened periodically, it always got looser over time. That might have been enough information by itself..

Eventually it got sticky and I could no longer access the tallest 4 gears, even though the rear-derailleur seemed to have enough spring and the brifter would shift if I pulled on the cable. But it wasn't road-worthy, so then I had to get off my lazy duff and find out what was wrong.

The shift cable was frayed inside the brifter housing, and was down to 2 strands. I cut it, removed and replaced. $5 and half-hour later, it was all tuned up and shifting easily from top to bottom.

I presume it will last a long time, and stay in tune a lot longer. But how does a shift-cable get chewed up inside the brifter anyways? It seems like it had to have been a faulty cable or someone pinched it hard during installation. (Used Windsor bike I bought almost new in 2008.)

if you never shift the cable wont break. as you shift the cable bends back and forth. think bending a paper clip over and over, eventually it breaks

You are fortunate that you didn't wait until the cable broke; getting the broken end out has made grown men cry. You should check the other cable NOW even though it typically does not see as much use and then both periodically and/or when it starts misbehaving again.

I have a set of Ultegra 6600 brifters (vintage 2008) and as part of my maintenance routine, I replace the wire every 9 months to a year. I'm guess it's a poor design, and the wire might be bent over a sharp point and as retilezs pointed out, the metal fatigues. I'm guessing if there is a smooth, radiused feature for the wire to bend over, it would eliminate the problem.

Best thing to do is replace the wire at some regular interval. And keep an extra wire or two in your tool box.