"Last Time By" in Softball

[Manny A]

I'm curious which softball organizations recognize the "last time by" concept that I learned over in that other sport when I umpired there. Here's an example:

R1 on first base. She takes off for second on a hit and run. The batter hits a deep fly ball into the left-center field gap, and R1 touches second and takes a few steps to third, thinking the ball will fall. But then as she looks, she sees F8 make a crazy catch against the fence. R1 heads back to first, but misses second on the way. F8 throws the ball in to F4, who turns and whips a throw to F3, but the ball hits R1 in the helmet as she dives into the base. The ball ricochets toward the fence down the first base line, and R1 takes off again. She touches second base and beats the throw to third.

The defense then appeals that R1 missed second base on her way back to first base. Is the appeal upheld? Or is it denied since R1 did touch second base on her "last time by" the bag on her way to third?

I don't have access to my rule books right now, so if you can cite a rule that applies here, I would appreciate it.