According to Allan Lichtman's Keys to the White House theory, Republicans went into the 1988 election with only three negative keys against them. That's a very strong advantage. I'll try to stay away from "The economy goes into recession two years earlier."
*Republicans held 177 seats after the 1986 midterms and 165 after the 1982 midterms. If they lose sixteen additional seats in 1986, they lose the midterm key. Before the midterms, Reagan's position was that the weapons transfers had indeed occurred, but that the United States did not trade arms for hostages. If Reagan doesn't wait until March of 1987 to take full responsibility, maybe Republicans do worse in the midterms.
*If real per‑capita economic growth during the second term doesn't equal or exceeds mean growth during the previous two term. It was down during Reagan's second term. Maybe if it lags a little more. That would be a better indictment of Reaganonomics for Democrats to run again.
Beyond that, it gets tricky.
*A protracted nomination contest would work. Let's say George Bush bungles his interview with Dan Rather, then he loses New Hampshire to Bob Dole. But is it really realistic that at a certain point, Reagan wouldn't put his thumb on the scale?
*If Democrats bring articles of impeachment against Reagan, that brings the scandal key, although an inadvertent side effect might be Reagan resigning, which would hand the Presidency over to Bush, who would then run for re-election. Democrats would lose their advantage of running against someone who isn't an incumbent.
*Hard to see a historically charismatic Democrat throwing their hat in the ring.
*Someone else would have to inform me on the likelihood of this but the Russians lost Brezhnev, Andropov, and Chernenko in just a few years. Is it possible that one of them survives, adopts a different position than Gorbachev, and the Cold War continues onward?
Looks like a recession or a third party candidacy (Trump '88?).