Before I attempt to explain whyy Mississippi is a Republican stronghold today, let's describe another state - call it State X. Looking at State X is very useful for analyzing why Mississippi votes Republican. I invite you to guess what state it is.
Here is a description of State X.
Demographically, State X is very rural and very white. There are no major cities in the state; one has to cross state lines and drive more than a hundred miles to find the nearest metropolitan area. Racially, the state is homogeneously white; indeed, it is the second whitest state in the entire nation.
State X has almost always been a one-party stronghold, and that party has generally been the Republican Party. The Republican Party has almost always taken this state's electoral votes; indeed, it voted for a Republican president for more than a century. State X has only elected one Democratic senator in its entire history.
I am talking, of course, about Vermont.
Despite its history of supporting Republicans, Vermont is currently a one-party Democratic stronghold. In 2008 it gave President Barack Obama 67.5 percent of the vote. It currently sends Socialist Bernie Sanders to the Senate (in addition to Democratic Senator Patrick Leahy, the only Democrat the Green Mountain state has ever sent to the Senate).
What does this have to do with Mississippi voting Republican?
Well, Vermont and Mississippi almost never vote the same way for president:
Indeed, there are only seven elections out of 48 total (since Mississippi became a state) that the two have supported the same candidate for president: 1820, 1840, 1872, 1972, 1980, 1984, and most recently 1988.
Oftentimes during presidential landslides, Mississippi or Vermont are the only states which refuse to go along with the rest of the country. In 1936 President Franklin D. Roosevelt won an enormous landslide, taking the highest percentage in the electoral vote since the beginning of the two-party system. The only states to go against him? Maine - and Vermont.
In 1964, on the other hand, President Lyndon B. Johnson likewise won a stunning landslide, taking the highest percentage in the popular vote - again, since the beginning of the two-party system. This time, however, it was Mississippi that went against the president.
In 2012, barring an epic meltdown on either the Democratic or Republican nominee, Mississippi will vote Republican and Vermont will vote Democratic. This trend is likely to continue as far as the eye can see into the future.
It seems that there is just something that drives Mississippi and Vermont different ways. Vermont is a symbol of the Yankee North; Mississippi of the Deep South. Since the founding of America, the two have been culturally and socially at odds. Sometimes this division occurs in trivial ways, such as nasty stereotypes or different voting patterns. Sometimes the division takes on much more significance, most famously in the Civil War.
So to answer the question in the post's title, Mississippi votes Republican because Vermont votes Democratic. Or, to put it another way, Vermont votes Democratic because Mississippi votes Republican. And as long as presidential elections continue to happen, Mississippi will probably be voting the opposite way of Vermont.