Hi Aurore, the chitosan matrix should be stable in most buffers with a pH > 7.
As for your results from the BCA assay, the BCA reagent reacts with amide bonds. Chitosan is derived from chitin, which has acetylated N-linked sugars, e.g. amides.
The process of converting chitin to chitosan is to deacetylate the chitin. This not a perfect process and there will always be some amide groups left that can react with the BCA reagent.