I'm not very familiar with the TA06, but back when I was running my Mini, I replaced the kit servo saver with the Tamiya blue upgraded one. With both servo savers, I was having trouble driving the car down the straight. I finally found that both the kit and upgrade units had a bit of free play and sort of a "click" just as they come back to center. Much like you're describing, the unit would turn left, but not quite back to center unless you gave it a nudge with your fingers. With mine, it would do this in both directions though.

I took the new one apart, looked at it for a minute and simply replaced with with a Kimbrough Mid-Size servo saver for $7. I didn't have any problems after that. My daughter was having the same trouble with her Mini as well using the kit piece.

Not sure what the TA06 uses, but if they happen to be the same servo saver as the Mini, I'd look there for starters.

Good luck