In general, a two-party system will evolve such that both parties control ~50% of the relevant votes averaged over multiple elections. Individuals might stick to their principles and refuse to compromise, but parties are not so limited.
Losing a solid voter base might mean that the Republicans need to change their platform to appeal to more voters, but it doesn't mean that they're forever doomed and will never win another election. Maybe that means compromising on abortion. Maybe it means immigration reform - but from the Republican perspective, and not giving amnesty to illegal immigrants. (And funnily enough, IIRC amnesty isn't particularly popular among LEGAL immigrants) Maybe it means pulling their heads out of their asses re: climate change, and running on a revenue-neutral carbon tax.
All of this means changes, but not an end to the party.
I don't disagree with you. I think the question is, how much will the Republican party be willing to compromise on (immigration [1], abortion [2], social safety nets [3] [4] [5], drug reform, income and wealth inequality, discrimination) before they're no longer Republicans in order to gain enough votes to remain relevant.
As you said, neither party is going away, but they will both have to change to accommodate an evolving electorate. As someone said upthread, both parties need to stop taking their voters for granted and go out and listen to them.
Losing a solid voter base might mean that the Republicans need to change their platform to appeal to more voters, but it doesn't mean that they're forever doomed and will never win another election. Maybe that means compromising on abortion. Maybe it means immigration reform - but from the Republican perspective, and not giving amnesty to illegal immigrants. (And funnily enough, IIRC amnesty isn't particularly popular among LEGAL immigrants) Maybe it means pulling their heads out of their asses re: climate change, and running on a revenue-neutral carbon tax.
All of this means changes, but not an end to the party.