You have no need to do anything. By contacting the author, you pointed out what you believe to be a flaw. It could be you are incorrect, it could be that they deal with this in a future version, it could be that they simply don't care. To me, this situation is akin to the following xkcd comic:
People perform research, good and bad, every day. Once it's published you can feel free to write an article refuting their conclusions, but until then it's just informal academic discussion, and there's nothing you can really do about someone else being wrong.
Disclaimer: Some disciplines may treat preprints as actual publications, and if so, the preceding does not apply. I do not know of any fields for which this is the case, but then again, there's a lot of things I do not know.