They do sometimes cheat this rule by trying to bring back the first villain as often as possible, regardless of whether the villain died in the first movie. They'll film flashbacks if necessary. Lex Luthor, Magneto, Dr. Doom and the Green Goblin have all appeared in nearly every single film in their respective franchises--two of them returning from on-screen deaths, proving that nothing is impossible in a world where big box office dollars are at stake.
Interestingly (or bafflingly, depending on your point of view) the villains often turn up in a predictable pattern: the Brain, the Bod and the Bumbler.
Ms. Teschmacher (the Bod) Otis (the Bumbler) Lex (the Brains)
The Brain is the planner and nearly always creates the main conflict the heroes must resolve. However, since the plan is usually very simplistic and takes about two seconds of screen time to explain, the Brain spends most of their screen time heaping verbal or even physical abuse on the Bumbler.
Bod -> Brains -> Bumbler
The Bod is usually there to show cleavage, wear tight leather pants and show partial nudity. Some market research suggests this appeals to comic book fans.
The Bumbler began as just that, a character who shuffles around, usually screwing up the simplest of assignments. However, this role has evolved into a mute or retarded character with great physical strength but little in the way of brains. However, they are still the target of jokes and abuse by other characters. Plus, they often provide many of the film's comic relief which may or may not be gut-wrenchingly awful.
No one knows why this formula has been used so often. Perhaps it is some sort of primal urge in humanity where the three faces represent the three ages of man. Or, perhaps there's some deep psychological comfort in triangles or groups of three. Maybe it's a subconscious representation of the Holy Trinity or a subliminal image of the Masonic Pyramid.