How many times is this that you've broken your promise? I am reasonably sure that "How many times does this make it that you've broken your promise?" is correct. However, both sound fine to me and I can't be sure that the former is grammatically correct.
Both your attempts seem rather clumsy. The original edit had the phrase "including this time" implying that the promise has been recently broken, again.
You could ask the question
How many times have you broken your promise now?
which includes the most recent.