Minorities only like the Democratic Party because the Democratic Party panders to them and they believe in affirmative action instead of hiring a person based on their skill. The Republicans are not very popular with minorities because the Republicans don't pander to their every whim.
True, the only problem is that in supporting that position the Republican Party also panders to a base of voters who would like to use skin color as a reason not to hire someone. A very large and vociferous portion of the Republican base consists of people who use terms like "real America" when talking about lily white rural communities and question the citizenship of a man whose mother was born in Kansas and whose grandfather served in the US army during WWII.
So, I don't see why its a mystery that minority voters prefer not to align themselves with a party whose supporters are offended by the very presence of minorities in this country. Until the Republican Party base becomes more tolerant, minorities will continue to vote with the Democrats.
Stealing the South from the Democrats turned out to be a brilliant short-term strategy for the GOP when LBJ ended the Democratic alliance with Jim Crow. Now, its coming back to bite the Republicans in the ass.