In the First Age, when the Elves first awoke and were terrorized by Morgoth, the Valar came to help as soon as they learned of it, defeated and captured Morgoth.
When the Noldor went against the will of the Valar and followed Morgoth to Middle-Earth, and were eventually defeated by him, the Valar listened to Eärendil's pleas and began the War of Wrath, defeated and captured Morgoth.
So if Gandalf and Frodo had failed, would Sauron really have had complete dominance forever? Or would the Valar have intervened again? If not, why? Is it because in Arda Marred, the Valar are not able and/or willing to directly intervene anymore, and sending the Istari was all they could do?
Are there any statements in Tolkien's writings about this?