The Gulf kingdom is believed to have felt even more isolated after its main regional ally, the United Arab Emirates (UAE), reduced its military presence in Yemen in 2019, in a bid to reduce its losses there.
A Western official familiar with the kingdom's policy in Yemen said that "like the UAE, the Saudis want to say this war is over for us, but the situation on the ground is very difficult."
Recently, the Houthis have been able to seize large areas in the strategic governorates of Al-Al-Jawf and Marib north of the country near the borders with Saudi Arabia, which would enable them to launch air strikes within Saudi territories.
However, several experts believe that Riyadh is still capable of putting an end to the devastating war in Yemen.
A research fellow in the Bernstein Programme on Gulf and Energy Policy at The Washington Institute, Elana DeLozier, said: "The Saudis are in the best position to do this [end the war] because they have relationships with all the major players in Yemen."
However, she warned that "Saudi Arabia's ability to manoeuvre and end the war on acceptable terms may be diminishing."
Thomas Juneau, an associate professor at Ottawa University, Canada, said in an analysis published by the Sanaa Centre for Strategic Studies that "Riyadh believes that its sudden withdrawal will weaken the coalition or lead to its disintegration, which serves the Houthis and their external support, Iran."
He explained that at the same time, "Riyadh wants to reduce the costs of its intervention in Yemen after it has realised that it cannot afford the war's financial and military costs in the long run."
So far, there have been no signs that the war in Yemen may come to an end which Saudi officials have confirmed is key to countering "the threat of Iranian expansion."