The Benedicks-Carleson theorem on the existence of strange attractors for Hénon maps is an example, I would say. Over the years, there have been some attempts to give improved presentations of the proof, but I don't believe there have been any dramatic simplifications. (However, I am not an expert in this precise area of dynamics.)

Nb. The paper was published in January 1991, which date misses your 25-year rule by a few months. However, the paper was received by the journal in 1988, and revised in 1989, so I shall invoke those dates to argue for its eligibility. ☺