For a number of reasons I think:
1. Cubans have been a Republican constituency in FL for a long time, and it is only now beginning to change as a new, more Democratic generation of Cubans replaces them
2. Republicans on average have over a 20 point lead among white voters, and while not nearly as large as some other Southern states, it's large enough. Republicans made a +5 point gain among white voters between 2008->2012, and arguably their best showing among whites in a generation or more.
3. The primary driver behind Republican success right now in FL is older white/Cuban voters, and Florida has a lot of them. Right now it is the most elderly state in the country, and that, in combination with migration trends of old people => FL, has help Republicans offset demographic changes and their inevitable political ramifications.
4. African Americans punch below their weight here as FL's permanent felony disenfranchisement policy has led to something like 24% of the adult African Americans being unable to vote. They comprised 13% of the electorate in 2012 despite being 16.7% of the state's population. This is out of whack compared to other states with lax felony disenfranchisement policy, where blacks actually tended to match or exceed their share of the population in terms of voting.
However, there is, in my opinion, every reason to believe that the bottom is going to fall out for Republicans in the coming decade(s):
1. The new(er) generations of voters in FL are heavily diverse and heavily Democratic, and the ones that follow will be just as diverse:
2. Puerto Ricans fleeing the island are speeding up demographic political trends in FL
3. Younger Cubans are not staunch Republicans like their elders, and Cubans in general are shrinking as a size of the state's Hispanic population
4. There is a push to end permanent felony disenfranchisement in the state and may result in a ballot initiative in 2018, of which could substantially help African American voting power here.
5. College+ educated voters in FL are not only growing as a part of the electorate, but Democrats have been performing better and better with them for a while now, and they tend to be more reliable than less educated parts of the population. This is in line with national trends, and may have something to do with the growth of Millennials as a part of the electorate.
Honorable Mention: The fact that the state Democratic Party is a complete and total disaster and has been since Lawton Chiles died.
