High tension on the pull-pull could possibly do it, but what is more likely is that it puts tension on the servo shaft and bearings where it just doesn't need to be that tight.. certainly not guitar string tight, but not loose enough to have a droop. You should easily be able to replace the servo to see if that is the problem. I'd adjust the tension so that it's not "tight", check it, if it continues, swap out the servo and give that a quick try.

CGr