Previously, the Saudis had lobbied hard to get seat at the Security Council and reportedly even tried to buy Syria's seat when it was given to them a few years ago. So when the Saudis first rejected the seat and a good number of Islamic States openly petitioned the Saudis to reconsider and take the seat, it appeared that Saudis were simply being cleaver traders by way of creating a situation whereby they could say to the Arab world; "OK, we'll do you a favor and take the seat."
But now it appears that they really aren't going to take it and this brings up two possible reasons, both of which involve a desire to actually avoid any further international attention to themselves at this time.
1. The house of Saud is increasingly dysfunctional causing the Saudis foreign policies to become almost as erratic as that of the U.S. The most consistent element in the Saudis foreign policy is the Saudis continued ability to be duplicitous on almost every issue. With the political chessboard in the Middle East now is such a state of change, the Saudis may view having to publicly commit themselves to one side of any issue brought before the Security Council, to be very difficult and limiting to their usual ways of political diplomacy.
2. In the same way, the Saudis don't want any further attention paid to their domestic policies. When the UN actually took the step to reprimand the Saudis for the regular kidnapping, rape, torture and murder of individuals within the Kingdom, the Saudis promised the UN to .... blah, blah, blah. More than a year later the domestic repression has actually been ratcheted up. So a seat on the Security Council might be viewed by the Saudis as potentially having unhappy UN members rekindle discussion of their darker domestic policies.
In short, we all know the Saudis are snakes that like to live and work in the shadows. They're not particularly comfortable having bright lights focused down upon them.
