You can find hundreds of explanations for why the Republicans lost the most recent elections. I think the simplest explanation is that the conservative movement has developed an ideology that is basically hostile to the idea that the federal government should do anything. And that is tough for a candidate for federal office. Another contributing factor is lack of sincerity. If you take an issue like public education, this becomes pretty obvious. I can run for federal office saying that the federal government should have a smaller role in setting education policy. In essence, I am passing the buck. I am saying that you should go ask your state senate or state assembly candidate what they think about your local schools. That might fly with a concerned parent if the local Republican candidates have a robust plan for improving the schools. The problem is that the local candidates don't have any answers.
The GOP sends a message that they are for more local control but they don't really mean it. They are opposed to public education regardless of what level of government is making the decisions.
The result is that they have no solutions. They run for office but they have nothing to say about what they would do if they win. You can argue that voters prefer Democrats because they want free stuff, but what they really want is someone who will take some action to improve things. The GOP is no longer is willing to even pretend they want to use the government (on any level) to solve problems.
I think that is why they lost and it is also why they will continue to lose.