Why did the battle with Amalek go back and forth depending on Moses' arms?
The battle went back and forth because God was in control, using Moses' uplifted arms as the providential sign. As long as Moses' arms were held up, Israel prevailed; when they fell, the battle turned against them. This showed God fought for Israel, and Moses named the altar Jehovah Nissi, 'He is our banner.'
Les explains that although God used the Israeli men to fight, God Himself really fought the battle against Amalek. The account was so providential that as long as Moses' arms were held up, the battle went on Israel's side, and if it fell, it went against them. This demonstrated that God was in control. Afterward Moses built an altar and called it Jehovah Nissi, which means 'He is our banner,' like a flag or marching flag. Les connects this to Zechariah's statement that Christ will return and fight against the nations as when He fought in the day of battle.
And it came to pass, when Moses held up his hand, that Israel prevailed: and when he let down his hand, Amalek prevailed.