There are some senses of "much" and "many" that are restricted to non-affirmative contexts, and when "much" and "many" are used in that way then they are negatively-oriented polarity-sensitive items (NPIs).
There are some senses of "much" and "many" that can be used in positive affirmative environments, but then those instances of "much" and "many" are not NPIs.
And then, to make things even more confusing, some words (such as "much" and "many") may be an NPI in some styles or registers and not in others.
This issue with "much" and "many" is discussed in the 2002 CGEL, pages 823, 826-7. There might be some related info about NPIs on the internet, such as in wikipedia or on linguistics sites, but you've gotta be careful of info found on the internet.
If you want more info here in this post, then leave me a comment and I'll try to come back later tonight. (The reason why this post is now so brief is that many topics are involved and I'll have to discuss them as a foundation for this topic that you are asking about.)
Note that CGEL is the 20002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language.
Best Answer
There is more in that question than meets the eye.
Much is correct in the affirmative (a large quantity or amount, see American Heritage). It so happens that it is a) slightly archaic b) not often used with concrete words (water, butter, etc.) or ordinary quantities (money). Hence that would sound a little passé in normal conversation:
Compared to:
My best guess: much still belongs to an educated register and more likely to be used with set phrases:
Aside of much + comparative, which also belongs to spoken language:
By contrast a lot is informal and not particularly advisable in written style. One would write:
A lot did displace much but that leaves an awkward gap in formal language, requiring clunky periphrases. Hence I would argue that:
still does have its place in formal style, for brevity. But that would probably be a matter of opinion.