For most of the 20th century, West Virginia leaned Democratic (the big gap in 1924 was presumably because the Democratic nominee was from West Virginia). In 1988 it was one of only ten states to go for Michael Dukakis. Since 1988, the relative Democratic vote has dropped in six straight elections, and the state is now strongly Republican.
The fact that the change didn't start until about 1990 suggests that it's not primarily about race, and its steadiness since then suggests that it's not primarily about the personal qualities or styles of the candidates. So what caused it? I'll offer a hypothesis, although I don't have time to test it: voting participation has fallen among people with low income and education as mining and factory work has given way to unemployment or irregular employment. So an increasing share of voters are middle-class people who disapprove of those who are on "the draw."