Between the left-wing and right-wing bases, only one of them is demographically being put into decline while the other massively benefits from immigration and birth rate.
How does immigration necessarily support left-wing positions? If you look at eastern countries, and specifically much-maligned muslims, you see a multitude of super conservative positions. In fact, if all I (as a far left-wing person) care about are my world views having the largest share possible, I need to strongly opposed immigration from islamic countries, because traditionalistic, regressive, conservative views are dominant in many or even most islamic majority countries. Conservatives could very wellwork towards adopting a stance that integrates immigrants politically. In fact, take a look at the following statistic from Hessen's election:
Left: Non migrants, right: People who have migration experience. To explain the colours: The black bar is the conservatives, red bar the social democrats, green bar the greens, blue bar the far-right, yellow bar the neo liberals and violet bar the socialists. As you can see, the three right wing parties (black, blue, yellow) have posted a better result with people who have migration experience than those who do not. This is of course only a single data point, but if you take a look at the policies of popular politicians in majority-muslim countries in particular, you will find that they are not exactly left-leaning.
Anyway, if the majority opinion changes, so should the outcome of elections. If this is not the result of majority opinion changing, then something is wrong.
If it is true that the republican party line is being diminished, what will happen is one of three things:
(1) a new right wing party will establish that manages to better adapt to the time
(2) the republicans change their course to attract more voters
(3) an existing party increases its mind share.