Lookback clarification

[BretMan]

Another Look Back question:

Runner rounds first base as pitcher gets ball in the circle (ie: LBR is in effect).

Runner stops momentarily off first, then immediately proceeds to second base (all legal, so far).

As the runner reaches second, she rounds it. Upon rounding second, she stops momentarily then immediately returns to second base.

Is the runner out for having made a second stop?

The rule governing her first stop (between first and second) says that she is out if she does not immediately return to first or advance toward second. The runner met that obligation.

Her second stop, after rounding second base, would not violate the spirit and intent of the rule. It would not be done as a jockeying cat and mouse game, but as a normal rounding of the bag and quick return.

As the LBR is written, the second stop or reversal seems only to apply when in between two bases. Once the advanced base is legally obtained, is there any sort of "reset" (for lack of a better word) to the runners Look Back obligations?

Is there any interpretation to cover the play I described, or is it simply "two stops, you're out"? I can see a logic and common sense to allowing that second stop after the advanced base has been reached.