The Targum Pseudo-Jonathan fills in what the Hebrew leaves implicit: why Moses's hands grew heavy. "The hands of Moses were heavy, because the conflict was prolonged till the morrow, and the deliverance of Israel was not prepared on that day; and he could not hold them up in prayer; on which account he would have afflicted his soul" (Exodus 17:12).
Moses was not simply tired. He was about to begin self-mortification, to fast and afflict himself further in anguish over the delay. The Targum shows a leader who blames his own unworthiness before he blames anything else. But Aaron and Hur intervened with practical tenderness.
They sat him on a stone — the Aramaic specifies that he took no cushion, only stone, so that he might share the discomfort of the soldiers below. Then "Aaron and Hur supported his hand, this the one, and that the other; and his hands were outstretched with firmness, (or, fidelity,) in prayer and fasting, until the going down of the sun."
Three things happen together: Moses fasts, Moses prays, and Moses is held. The Aramaic word for firmness, emunah, is the same word used for faith. Faithful hands do not hold themselves up. They are held up. The takeaway: the holiest moments of spiritual endurance almost always require two other people quietly doing the unglamorous work of supporting the one at the front.