In the movie Rollerball (1975), why didn't Jonathan quit?

Rollerball was a team sport. It emphasized team over individuals. Jonathan's fame made him an individual, rising above the team.

The central concept behind the movie was to be an individual, not a sheep. That is, to make a name for yourself and rise above the herd. It's sort of a Capitalist view, but that was what the author was trying to convey.

From outside the story, Jonathan couldn't quit or that would have defeated the storyline. From inside the story, Jonathan wanted to show the corporations that their ideals were wrong.

Here's an excerpt from the Wiki about a scene late in the movie that really nails the entire movie down to a few sentences:

The corporations hold an emergency meeting to discuss Jonathan's obstinate refusal to retire, and decide that the championship game against the New York team will be played without penalties, player substitutions, or a time-limit, in the hope that Jonathan, if he decides to participate, will be killed during the course of the game. The executives's meeting reveals why they are demanding Jonathan's retirement: Rollerball was conceived not merely to satisfy man's bloodlust, but to demonstrate the futility of individualism. Jonathan's singular talent and longevity in the sport defeats the intended purpose of Rollerball.

The ultimate point of Rollerball is that people had given up control of everything in their lives to Corporations that ran the world. The Corporations kept the people drugged to control them and used Rollerball to entertain them. It's a warning about the rise of a Corpratocrisy that gave rewards for compliance. Like the Roman bread and circuses.

I love this movie, a lot to process here-

1975 Rollerball is a little vague in my opinion, so could be interpreted in many ways. I find that the point of this film revolves around the cyclical nature of the human struggle. Jonathan doesn't quit because he begins to question the nature of his existence and the gravity that the sport Rollerball has in his world. He is looking for answers to why they want him to quit, what he would do if he quit, and how everyone ended up playing Rollerball anyway? When he goes and looks for information on how the world became this way, he finds that historical knowledge is being censored and all information is controlled by Zero, the "World's Brain" made of "fluid mechanics-fluidics" as one technician explains. A "memory pool" that all human knowledge and recorded history has been reduced to. Jonathan asks Zero for "Information about corporate decisions, how they are made and who makes them?". Zero is reluctant, but because of Jonathan's fame, the technician convinces Zero, telling it to "Make it simple, answer him".

Zero's response here is a key element to the overall theme of Rollerball as a film: "Corporate decisions are made by corporate executives. Corporate executives make Corporate decisions. Knowledge converts to Power. Energy equals Genius. Power is Knowledge. Genius is Energy. Corporate Entities Control All Fundamental Elements Of Economic Life. Technology, Capital, Labor, and Markets." -and Zero repeats, caught in a loop.

So either the Corporations created Zero and use it to brainwash and control the masses, or it is a rogue entity that could be the result of AI gone wrong, or may even have extraterrestrial origins. Either way, it is clear to Jonathan by this point that the world he knows is all a facade, an elaborate creation by the Corporations to prolong their own existence. The "game" of Rollerball was designed to demonstrate the futility of individual effort, and as Jonathan's manager remarks, "If a Champion defeats the meaning for which the Game was designed, then he must lose".

In fact, Jonathan does the opposite, he wins. He is the last man standing in the most brutal version of the sport that he used to love at the end of the movie, but hesitates from delivering the last killing stroke with the Rollerball itself, instead of scoring to simply "end the game".

TLDR

I think that Jonathan doesn't quit because sees his position as unique in that he has the power to unite the entire world into a revolution against the tyranny of informational control that Zero/The Corporations have over everything. By beating the Corporations at their own game he establishes control and breaks the cycle of their influence. Now the people will rise up and chant Jonathan, as he leads them to a new era of Freedom.

Jonathan cared about three things in life: his wife, his team-mates, and playing Rollerball. The corporations took his wife from him several years ago, now they want to take Rollerball from him. To pressure him, they change the rules of Rollerball, resulting in the death of his best friend and other team-mates. Jonathan is completely pissed off and wants revenge. He wants to spit in the the corporation's eye, and he has nothing left to loose.

Note that Jonathan doesn't appear to care very much about material rewards or the adulation of the fans. However, he does recognize that the adulation of the fans gives him leverage against the corporation. The corporation needs the population to stay obsessed with Rollerball, but not to think deeply about the power behind it. If they simply fire Jonathan they risk exposing the game as a system of social control, managed by the corporations, not an honest game. Of course that's what it actually is, but if the population has that fact shoved too obviously in their faces, it might stop working.