CaptDon's failure mode seems plausible, but I also somewhat doubt it's the case here. I have to imagine TV backlight drivers are designed a bit better than that, and if it were really hammering the strings with some fault you'd probably see more burn out while it is being tested and diagnosed.
As suggested earlier, the controller is probably just taking offense to the compliance voltage going out of range. The parts are cheap enough and failure common enough I'd probably just throw a new set of strips at it and call it a day, keep the backlight control away from maximum if you don't want to repeat the job. If one insists on diagnosing properly, check the forward voltage of the individual LEDs (some have multiple dies in series in one package), and tack diodes into the series strings to make up for the shorted ones, should stay lit then if nothing else is wrong. Just be careful as this runs at fairly high voltages, some are up around 300V.