Ah challenge: Sitting president runs as independent and wins

So at some point for whatever reason, the president's party drops him, he runs as an inpedendent and wins. How and when could this happen? How could this effect the political landscape?
 
Off the top of my head, 1948 is just possible. I mean, Truman had Thrumond and Wallace bolt on him as it was. Let's say Wallace is killed by a Nazi spy/assassin who can't get at FDR in early '44, so the presence of a plot is the POD. Without his influence, th4e left-leaning sides of the Democrats look for someone else. Truman becomes VP and then President, as in OTL, but Dixiecrats manage to wield enough power that, when Truman integrates the military, they push Strom Thurmond for the nomination.

Truman runs as in OTL, but he's the independent, and with the Wallace crowd preferring to back him rather than Thurmond, he wins much as in OTL.

Now, an election other than '48, I'm not so sure.

As to what it does for the policial landscape, probably not a lot. Enough people were bolting the Democrats in '48 who came back in '52 that the Democrats probably just realize they need those people, and make up with them. However, Eisenhower has an easy win, in '52, maybe easier than OTL.
 
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