It's with the square root rule as with all such rules: Don't merely follow it, but try to understand it. Statistics can be a bit counterintuitive, but I hope it's intuitively clear that just stopping and restarting your system is irrelevant for reinvesting.

So, I fear your person A will not keep her hard earned money, regardless of how often she stops and starts. Here's the formula to calculate how long the money will last, under "money management":

https://www.financial-hacker.com/build-better-strategies-part-3-the-development-process/

The square root rule is also explained in the black book and in short also in workshop 6.