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Explanation: The first sentence is incorrect English
The second is correct.
As to justification, English is my mother tongue and I can simply tell you that no self-respecting English person would even think of using the first solution. It would however work in "casual" speech in the form of "Why doesn't...." and there the abbreviated form of 'not' has to be stuck on the verb for obvious reasons. As the first sentence is written, it is however WRONG
From Hong Kong I was able to find more than 200,000 hits for the phrasing "Why does not". Unfortunately, I am not at all surprized. This and similar phrasing is commonplace in East Asia, and is likely to worsen throughout the world.