I think this is quite a subtle issue. I agree with @Thursagen that in OP's specific phrase, "why" is probably better. However, in this similar case...
- Is there some reason you don't want to come?
- Is there some reason why you don't want to come?
...I feel it's less important whether "why" is present or not. And insofar as I have an opinion at all, I would rather not include it.
This NGram has over 10,000 hits for "there some reason", of which it's obvious over half are questions that don't continue with "why". Plus 2670 for "there some reason why", which are nearly all questions.
In short, I think the distinction between "reason" and "reason why" largely comes down to individual style, and particular idiomatic usages.