Cycles exist, and conservatism will surely rebound; it just may be that the Republican Party will have died before conservatism revives. Conservatism could revive in a new party that appears as the Democrats split or in an existing Third Party (most likely Reform among existing Parties). Political parties can die, as did the Federalists and Whigs.
If the Republicans could survive the
Great Depression, at a time when they had less than 20 out of 96 senate seats, then they can survive almost anything. The Republican party is not about to "die" anytime soon.