Why does pepsin not remain active in the duodenum?

Yes. The precursor of pepsin is called pepsinogen; it is produced by stomach cells and then activated by the HCl in the stomach. Pepsin works best at very low pH.... e.g. acid conditions of the stomach.

The small intestine has glands that produce neutralize the acid. Pepsin denatures at pH's of 5,0 or higher..... so effectively it is neutralized when the chyme enters the small intestine.