Note that four of Nixon's eleven counties flipped in 1964.
I wondered about this very question somewhere...sometime...years and years ago...on this very forum. But didn't find a really satisfactory answer.
Don't try to find anything in modern-day demographic data - the county's population's mushroomed like all hell recently, meaning the people who voted there in 1964 have been submerged.
But yeah, one can only assume a typo or some civil rights / general opposition to Georgia politics thing. Is 1948 available for paying members?
What I found interesting just looking at the Wikipedia is:
The county has been creeping in favor of Democrats over the past 3-4 elections (when you look at gubernatorial at least; presidential seems to be mostly flat) and growing at a very fast rate (%) as well. I assumed that this was basically big McMansion growth flowing out of Savannah, but that statistic seemingly refutes it.
I haven't looked to be sure, but I know that the Gullah have increasingly been pushed out effectively of the islands in neighboring McIntosh County. Maybe they're settling in Long? That would explain the modest improvements for Democrats (and the rapid decline in McIntosh likewise) and the seemingly major drop in county income.