The Progressives don't collapse after losing in 1912. President Wilson goes to war with Germany in 1915 after the Lusitania is sunk. The Progressives try to draft Theodore Roosevelt to run again in 1916, and he reluctantly agrees after being refused by the Republicans. An electoral deadlock occurs, so the election goes to the House, which reelects Wilson. The post-war recession happens again, and communism becomes more popular than it was IOTL due to America being in the war longer. Roosevelt has died, so the Progressives nominate Robert LaFollette...who loses. However, after four years under a conservative Republican administration(possibly Warren Harding), the progressive factions of both the Democrats and Republicans, as well as many populist groups throughout the nation, turn to the Progressives in 1924, and young and charismatic Upton Sinclair is nominated, after two terms in the House of Representatives. He wins.
I know it's not exactly what you asked for, and I don't how plausible it is, but it's what I came up with.