No canonical proof
There are several reasons why one would think that Mad-Eye Moody died.
“We were just talking about Mad-Eye,” Ron told Harry. “I reckon he might have survived.”
“But Bill saw him hit by the Killing Curse,” said Harry.
“Yeah, but Bill was under attack too,” said Ron. “How can he be
sure what he saw?”
“Even if the Killing Curse missed, Mad-Eye still fell about a thousand feet,” said Hermione, now weighing Quidditch Teams of Britain and Ireland in her hand.
“He could have used a Shield Charm —”
“Fleur said his wand was blasted out of his hand,” said Harry.
“Well, all right, if you want him to be dead,” said Ron grumpily, punching his pillow into a more comfortable shape.
“Of course we don’t want him to be dead!” said Hermione, looking
shocked. “It’s dreadful that he’s dead! But we’re being realistic!”
(Harry Potter and the Deathly Hallows - Chapter Six)
- Bill saw him being hit with killing curse. He may have thought he saw the wrong thing in the rush of battle.
- He fell about 1,000 feet There are canonical spells such as Arresto Momentum which can save someone who falls off a broom.
- He didn't have his wand. Again we could doubt Fleur's testimony, but there are other answers as well. Wandless magic is something which is possible in the HP universe. Alternatively, someone else may have cast the spell, such as death eaters who intended to capture and torture him.
- Umbridge ends up with his magical eye If Mad-eye was captured by Death Eaters, they would have undoubtedly removed the eye, and he may have been unable to retrieve it before escaping. If he wasn't captured, it's still possible that it bounced out when he did hit the ground and he had to quickly flee the scene.
However, the main problem with him being alive is that he never appears again in canon, and Rowling has given no indications that he is still alive. So it's probably safe to assume (like all the characters do) that Mad-Eye dies, but there is no actual proof.
Out-of-Universe, the name of the chapter is Fallen Warrior, and Mad-Eye's death does serve a purpose in setting the tone of the story. These would all indicate that Mad-Eye died, but again not actual proof.