I think that corrosive skepticism is rather unusual a collocation in comparison to, i.g, corrosive criticism which is always directed towards someone causing unpleasant feelings, the adjective corrosive meaning spitefully sarcastic. As for skepticism, it refers to someone's own state of being unsure of something and so it is not directed towards anyone's feelings, can't affect or influence negatively as corrosion does to metals.
In addition, the "an ever more corrosive skepticism" part makes me think that the expression and its interpretation by the author were used earlier in the text. Maybe it has something to do with the external manifestation of skepticism which, if you dig deeper, may be rather unpleasant and even corrosive. I'm not sure, though.