Let's face it. It's probably never going to happen BUT

[Mister Mets]

It seems to me the likeliest way this could happen is if a party has primary voters really out of touch with the center of the country. It's not likely, but it's possible with increased polarization and nationalization of politics.

It would be more likely to occur with Republicans, as appealing to white conservative Christian parents is enough to win some congressional races, but could keep a party out of national contention.

But it probably wouldn't be a complete eradication. It would be more like Democrats after the Civil War, when Grover Cleveland was the only president to win elections for the party in generations, or the Republicans after the great depression, when blowouts for Democrats sandwiched the Eisenhower administration.

For a party to get eradicated, you would need some major realignment, like the fight over slavery becoming much more significant than the divide between whigs and democratic-republicans. Given the rapid rate of technological change, this might occur. Maybe universal basic income causes it. Or some kind of fight about robot rights.