I have to give this to "The Discarded Seal of Ivan the Terrible" since both players were basically flawless in the temple, but failed to acquire the artifact due to an impossible layout. I mean they did everything right including running fast, taking all the necessary shortcuts, and Travis even made it back to the platform in the Pit.
But I have to say "Henry Morgan" comes very close to being one of my favorite losses. You just gotta love how Shem completes the Observatory objective in four seconds and grabs the earring with two seconds remaining. Both him and Ashley are excited despite not getting the grand prize. But the one thing that turned me off from this run was Ashley putting the key back into the tree and going into the Mine Shaft to be taken out. But I guess that adds to the lost.

Votes to win:
#234: The Golden Earring of Henry Morgan - 1
#317: The Discarded Seal of Ivan the Terrible - 1
Top 25:
25 - #306: The Lion-Slashed Jacket of Sacagawea
24 - #118: Ponce de Leon and the Lost Fountain of Youth
23 - #226: The Mask of the Man in the Iron Mask
22 - #135: Pecos Bill's Lost Lariat
21 - #116: Henry VIII's Great Seal
20 - #127: The Medal of Sir Edmund Hillary
19 - #330: The Mummified Hand of the Egyptian King
18 - #215: The Electrified Key of Benjamin Franklin
17 - #334: The Bullet-Riddled Handbag of Belle Boyd
16 - #129: The Golden Jaguar of Atahualpa
15 - #325: The Red Sash of Tokugawa Ieyasu
14 - #211: The Imperial Purple Robe of Empress Theodora
13 - #333: The Pearl Necklace of Gwalior
12 - #208: The Bone Necklace of the Blackfeet Chief
11 - #238: The Broken Wing of Icarus
10 - #132: King Tut's Cobra Staff
9 - #133: The Dragon Lady and the Blue Pearl
8 - #228: The Two-Cornered Hat of Napoleon
7 - #209: The Mush Pot Hat of Johnny Appleseed
6 - #240: The Priceless Portrait of the Polynesian Gir
5- #338: The Good-Luck Watch of Empress Eugenie
4- #231: The Leopard-Skin Cloak of Annie Oakley
3- #322: The Royal Torque of Queen Boadicea