Here's the thing, they don't need to operate as a party.
I don't know if you are American, if you are disregard this bit since it is me just explaining how the system works.
When an election occurs, there are actually six main elections with a bunch of side positions. You have the federal positions of President, Representative, and Senator. Then you have the state positions of Governor, State Representative, and State Senator. Each state has their own executive and legislative branches. Additionally, each Federal position except President is sent by the states to D.C. They are responsible to and empowered by their states.
So, why bring up the micro civics lesson? Well, if those internal struggles get significant the party will remain. but they would have no unified operation. But, they would also not dissolve or become inactive.
Rather, the states would be left largely on their own. Each kind of doing their own thing and operating on a state by state basis rather than as a single unified federal entity. If the federal party stops being able to function, the state-level ones retain their freedom. But in the end, they would not be operating as a unified party. And in the end, the Progs would in fact just be stamping their feet and demanding social justice and reparations. You are right it won't do any good. But if there is no way to reconcile the differences between the parties of the big tent which I mentioned in my post above this one... that is what happens. The Big Tent burns down, and the states will do their own thing until the federal-level party rebuilds the thing.