If you are wealthy enough to be in the prince’s inner circle, you are more likely to survive the Red Death for a little while longer.

The Red Death kills indiscriminately.  It does not care whether you are rich or poor, because it is a disease!

The scarlet stains upon the body and especially upon the face of the victim, were the pest ban which shut him out from the aid and from the sympathy of his fellow-men. And the whole seizure, progress and termination of the disease, were the incidents of half an hour.

The only way that you can escape the disease is to leave the county.  Prince Prospero figures out a way to do this, taking his closest friends with him.  He does not care about the poor people in the kingdom.  He is only interested in the rich.

When his dominions were half depopulated, he summoned to his presence a thousand hale and light-hearted friends from among the knights and dames of his court, and with these retired to the deep seclusion of one of his castellated abbeys. 

If you were poor, you would likely stay behind to die.  If you were rich enough to be one of the thousand closest friends of Prince Prospero, you might get a reprieve.  The abbey was well-protected from the pestilence, at least at first.  No one got in after they locked themselves in there.  They had enough provisions to last them until the disease was over.

Even the rich and influential could not escape the Red Death.  It found them in their seclusion.  They died even though they were locked inside the abbey away from the affected population.  No one could escape the Red Death.

Poe’s message is that being rich and powerful will not save you from death.  Prospero is naïve and arrogant. He does nothing to protect his kingdom, instead protecting his friends.  He would rather be holed up inside a wall with a bunch of toadies than do right by his people.

How does social-economic status affect whether one survives or falls victim to the Red Death?

When the Red Death starts spreading across Europe devastating the population, Prince Prospero gathers up 1000 of his closest rich friends and brings them to his castle.  He locks up these lords and ladies in the abbey of this castle to protect them from the disease.  He offers refuge to the wealthy in his kingdom as well as others like musicians, cooks, and servants who can provide the comforts he is use to.  It is for his amusement that he chooses the noblest and most important people to wait out the plague that is encroaching on his kingdom.   In the end when the plague shows up as a mysterious stranger to the masquerade ball, we learn that the social-economic status of a person cannot save them from the disease and death.  Money cannot spare you from the fate of the Red Death.  

How does social-economic status affect if one survives or falls victim to the Red Death?

In short, it doesn't. This is actually one of the central messages of the story: that neither wealth nor status can protect a person from every human being's natural and necessary end—death.

Prince Prospero has a lot of money, but this does not ultimately protect him. He has the ability to remove himself and one thousand of his most healthy and interesting friends to a distant abbey, far away from where the illness rages, and this cannot protect him either. He can afford to supply the abbey with anything and everything his guests might need or want, even the stuff of fantastic dreams they've never had, but nothing can remove him—or them—from harm's way because death eventually comes for us all. Money might extend one's life, but it can never render one immune to death.

How does socioeconomic status affect whether or not a person survives or falls victim to the red death?

Prince Prospero gathers a thousand of his friends, "from the knights and dames of his court," to wall themselves in his castle in order to avoid the plague. These are members of the upper class, the aristocracy. The Prince has the money, the ability, and the means (the castle) to organize this event. So, at the start of the story, it appears that having a socioeconomic advantage also gives them a better chance of avoiding the plague (red death). Poe is obviously critical of this elitist and immoral attitude. He emphasizes this attitude by illustrating how thoughtless the Prince's select community are. While the masses are dying beyond their walls, they throw parties and do not have a care in the world: 

The external world could take care of itself. In the meantime it was folly to grieve, or to think. The prince had provided all the appliances of pleasure. There were buffoons, there were improvisatori, there were ballet-dancers, there were musicians, there was Beauty, there was wine. All these and security were within. Without was the Red Death. 

However, in the end, the Red Death does infiltrate the castle walls. To be sure, historically speaking, those with more money have always had (and continue to have) access to better facilities, health care, etc. So, to put it bluntly, it can be an advantage to be rich. And in this tale, Prospero counts on that socioeconomic advantage. But in the end, it proves futile. Poe does not challenge the notion that this has historically been the case. But perhaps he is challenging the notion that upper classes should have such an advantage. As much as this is a tale of mortality and art, it can also be interpreted as a criticism of elitism and upper class insularity.