The Progressive Party under Theodore Roosevelt split from the Republican Party in 1912, but by the 1914 elections, Progressives were starting to drift back, and Theodore Roosevelt himself put the nails in the coffin of the party in 1916 when he refused to accept another presidential nomination; while a handful of individuals were elected under the Progressive banner in '12, '14, and even '16, by '18 the schism was over and most Progressives who continued in politics had returned to the Republican fold, or joined the Wilsonian Democrats.
Is there anything which could deepen the schism, and have it carry on longer, perhaps even into the '20s? The split wasn't precisely sectional: while the Progressives were strongest in the Northeast and Midwest, they made some significant showings in the Pacific states as well (given that the Progressive branch of the Republicans had a lock on California, in the person of Hiram Johnson and his machine).
Paradoxically, for instance, could an earlier death of Theodore Roosevelt, before 1916 keep it going on with him as a patron saint rather than a living breathing figure who could end the party?