Well, the monarchy is most likely safe until the peace between the monarchy and the clerics is broken. For the moment, Saudi Arabia stands as one of the only Arab regimes that did not make the mistake of trying to crush the religious heads. Historically this has rarely gone well in the long run, though it has allowed the secular dictators to have their heyday (which has clearly passed).
I would argue Saudi Arabia has three big factors that could eventually lead to destabilization and internal conflict, all or none of which could happen in the coming years.
-Oil: This is, of course, the big one. Saudi Arabia's economy only has two meaningful sides, those being the Hajj and oil. Only the Hajj is renewable (there's a sentence nobody has ever written before). Once the oil starts to falter, Saudi Arabia's already fragile economy will begin to fray at the edges.
-Wealth Inequality: A sleeping giant. People don't tend to think about this one, but Saudi Arabia has some of the worst wealth distribution in the world. Most people are quite poor, and the government is giving out a lot of universal welfare to offset this. If that were to be disrupted, or if a movement were to spring up from economic troubles, it could snowball into revolution.
-Secularism: The House of Saud's current arrangement with the Wahhabis is akin to riding a tiger. Any kind of reform or secularization started by the monarchy is risky for the simple reason that they only have to start preaching against the regime for it to all go to hell.