Saudi Arabia's rulers have long maintained stability with the help of welfare spending and subsidies. But as the oil dependent country's crude revenues sink, the world is watching for political troubles.

Social unrest in Saudi Arabia is unlikely to ratchet up significantly in the next few years, analysts tell CNBC. But if crude prices remain low, and Saudi finances continue to deteriorate, King Salman bin Abdulaziz may find it more difficult to tackle civil unrest in the future.

Falling revenue could exacerbate dissatisfaction among religious minorities, the upper class, or royals, analysts said. Read MoreWhy OPEC's plan to balance oil markets backfired Saudi Arabia is the chief architect of OPEC's policy of maintaining crude output at roughly 31 million barrels per day, a level that has forced producers of higher-cost hydrocarbons — including the United States and Russia — to balance an oversupplied market through production cuts. But as U.S. and Russian drillers prove more resilient than most industry watchers had expected, oil prices have stagnated, putting pressure on Saudi finances.

On Friday, the Organization of the Petroleum Exporting Countries agreed to continue its current policy, sending crude futures lower. On Monday, internationally traded Brent crude fell below $41, to its lowest price since February 2009.

Last year, Saudi Arabia announced a $229 billion budget for 2015, its largest ever. As a result, the International Monetary Fund projects a 19.5 percent deficit for the kingdom this year. To cover the gap, the nation has burned through about $91.5 billion of its reserve assets, reducing total foreign reserves from a peak of $746 billion last August to a still-healthy $654.5 billion in September, according to the IMF.

In August, the Financial Times reported that Saudi Arabia was seeking to sell about $5.3 billion in sovereign bonds per month through the end of the year. The Saudis' borrowing ability is considerable, but they could find themselves mired in debt, just as they did in the 1990s and early 2000s, said Matthew Bey, energy and technology strategist at Stratfor.

From a social perspective, one thing to keep in mind is that the perception of Saudi Arabia as a wealthy country is false. You have an increasing number of poorer Saudis in the country who feel disenfranchised in an environment in which the politics of the country are changing. Hani Sabra head of Middle East and North Africa practice, Eurasia Group

If low oil prices and high spending persist, the Saudis will be forced to reduce spending on social programs, energy subsidies and education, Bey said. The challenge for the royal leadership will be making reductions in areas that will not elicit social backlash, he added. Saudi Arabia "is still a security state. It will rely on its social apparatus to manage unrest going forward," he said. Reached by CNBC, the Saudi embassy in Washington did not have immediate comment. Read MoreBiggest cash issues for Saudis is getting bigger

A reduction in subsidies would have domestic political consequences, and may affect the royal family's tacit social compact with the country's elite, said Simon Henderson, director of the Washington Institute's Gulf and energy policy program. Henderson asserted that most Saudis are conservative and do not desire social change. "They look at the chaos in the rest of the Arab world with horror," he told CNBC in an email.

While Saudi Arabia is by no means on the verge of collapse, risks are currently under-appreciated, said Hani Sabra, head of Eurasia Group's Middle East and North Africa practice. "If you look at the Achilles heel of a lot of countries in the Arab world, they have had a pact with people. You get cheap gasoline and energy, you live in a welfare state, and you don't open your mouth," Sabra said. Like almost every predominantly Arab country, Saudi Arabia has a Sunni Muslim majority. But it faces ongoing protests from members of its Shiite minority and long-simmering dissatisfaction among Muslims who do not subscribe to the strict, conservative brand of Sunni Wahhabism embraced by the monarchy. Earlier this year, the BBC documented three years of continuous demonstrations in an eastern, largely Shiite region that sometimes turned violent. Activists frequently cited poor economic prospects for residents in an area that is home to the Ghawar oil field, the largest conventional field on earth.

"From a social perspective, one thing to keep in mind is that the perception of Saudi Arabia as a wealthy country is false," Sabra said. "You have an increasing number of poorer Saudis in the country who feel disenfranchised in an environment in which the politics of the country are changing." The fractured nature of opposition groups works in the royal family's favor, Sabra said, but the current political climate is also breeding dissatisfaction at the top. Following his ascension to the throne this year, King Salman named his son, Mohammed bin Salman, deputy crown prince — making him second in line in the Saudi succession — after earlier appointing him defense minister and chairman of the country's economic council.