I have had a similar problem before, my car would lose steering late in the run the fix was going to a harder front tire such as a black, purple, or Ulti X-Hard and saucing more of the tire or for a longer soak. My theory was that the harder compound would wear the sauce off a bit slower and the extra soak would give it similar grip. Hard front tires also seemed to be more consistent over the course of the day, as I typically am lazy and run the same set practice, quals, and race.

Might be worth a shot.