It is an excellent question and I haven't ever heard a sufficient answer because there is none. I've struggled with it for years and have concluded there is no acceptable answer, other than it's a plot hole.
I'll address the answers given and explain why it's simply a plot hole:
Answer 1) Harry didn't put up a fight in the forest, he let himself be killed by voldemort so it doesn't constitute a real defeat.
-That makes absolutely no sense. Dumbeldore did not put up a fight against Draco when Draco disarmed him. Dumbeldore wanted to be killed, which would happen either by Draco, or if not Draco then by Snape. Dumbeldore gave no resistance yet the wand considered him defeated. This is the exact same scenario, yet the ownership transferred to Draco. Fighting or putting up a defense is not requisite for losing a wand
Answer 2) Harry didn't actually die in the forbidden forest just Voldemorts piece of him.
-You don't have to die to lose possession. You only have to be defeated and a minor defeat at that. Dumbeldore didn't fight back at all and didn't die to lose his mastership over the elder wand. Draco lost it to Harry and all Harry did was take Draco's wand out of his hand, and it wasn't even the elder wand, but his other wand, there wasn't even a fight. Draco didn't die and he lost mastery over the elder wand. Harry clearly lost the fight in the forest whether Harry defended himself, fought back or wanted to lose is immaterial. What part of Harry died, is also immaterial. Since death is not a necessary factor in winning a wand. Voldemort should have become its master at that point.
Answer 3) The wand chooses the wizard.
"You still don't get it, Riddle, do you? Possessing the wand isn't enough! Holding it, using it, doesn't make it really yours. Didn't you listen to Ollivander? The wand chooses the wizard . . ." (Deathly Hallows -- Chapter 36)
But usually what they're referring to is at the time of the purchase. But winning a wand is seems to be a relatively simple process. Ollivander states: :
"In general, however, where a wand has been won, its allegiance will change.” Harry Potter and the Deathly Hallows, Chapter Twenty-Four (The Wandmaker)
-Harry won possession of the Elder wand by simply taking Draco's other wand, not the elder wand, out of his hand at Draco Manor. So it doesn't take much to "win" a wand. The wizard doesn't even have to be in possession of it at the time. Winning a wand trumps the initial choice of the wand, it's allegiance changes.
Answer 4) It wasn't really a defeat, redundant.
-This would be the best explanation in that the elder wand refused to kill Harry. But again the Elder wand had no problem casting spells at Harry. The piece of Voldemorts soul did end up in Purgatory but so did Harry's. So the wand did affect Harry. Dumbeldore even told him he could move on or choose to go back, choosing to go back means that Voldemort using the Elder wand sent him someplace else, easily a win. It wasn't as if just the Voldemort part of harry went to Purgatory Harry did as well.
Harry Potter and the deathly hollows:
Harry Potter: I have to go back, haven't I?
Professor Albus Dumbledore: Oh, that's up to you.
Harry Potter: I have a choice?
Professor Albus Dumbledore: Oh, yes. We're in King's Cross, you say? I think, if you so desired, you'd be able to board a train.
Harry Potter: And where would it take me?
Professor Albus Dumbledore: On.
So the elder wand in Voldemorts possession sent Harry to the exact same place it sent the piece of Voldemorts soul that resided in Harry. Harry elected to come back to the world of the living. Again it doesn't matter whether the elder wand would deal Harry a fatal blow or not, it just needs to be a "win" which it clearly was.
It is an excellent question and there is no acceptable answer for why ownership of the elder wand didn't pass in the forest to Voldemort. It should have. I've addressed every answer given on the site, or the I've ever heard thus far. I eagerly await somebody to adequately find a solution to this so I can reconcile this issue. So my answer is that it's a plot hole, and a large gaping one at that.