If your using the Kelly optimum as your method of bankroll growth, what you do is not stop betting but change your Kelly opt.%
In my experience i know that i will run into my minimum Bankroll somewhere around the 40th bet in a betting series of 100. So I adjust kelly Opt% accordingly (less than 50%)until the minimum bankroll window has passed,I then adjust the Kelly Opt% to over 50% for the remaining betting series.
My own oddsline is also incorporated into the above...but that another story..