There has been some scientific research on this and it's both unclear and then I think it's from a replication standpoint they've struggled. They would do some experiments where they would like give someone a tough math problem, an impossible math problem, and see how long it would take them to give up on the math problem. So I think that that matches the sort of common sense or the gut instinct which is that yeah, that we have a finite amount of discipline.
Author Ryan Holiday talks about his book, Discipline Is Destiny, with EconTalk host Russ Roberts. Holiday discusses the mentor who taught him discipline, the self-control of Queen Elizabeth, the world-champion boxer who counseled the man who defeated him in the ring, and the forgotten Roman emperor who helped make Marcus Aurelius the man he would become.