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The supreme court can overturn precedent. They are not bound to follow the precedent of previous supreme court rulings. They don't do this lightly or particularly often, though.

How do appeals work with circuit splits? Suppose I lose a case, appeal to the supreme court, and am rejected. Years later, a different case in a different circuit reaches a contradictory conclusion, but the losing side declines to appeal. Can I now re-appeal to the supreme court in light of the split, or am I SOL?

You need to have a current case in order to appeal it. (Indeed, you need to have had a sufficiently recent adverse decision of an appropriate kind in your case in order to appeal it.)

Wikipedia's article is fairly complete: https://en.wikipedia.org/wiki/Precedent

TL;DR: Precedent is binding to court where it was set and "below". To overrule it, you generally must appeal until you reach the level above where it was set. IANAL.

Or non-significant early cases where the stakes aren't too high and rulings that will lead the path to precedence can vary.