I think there are two different questions in this thread:
(1) When should the Axis be allowed to re-do a battle and keep the second set of results?
(2) When should the Axis be allowed to walk away from a losing position without any sense of shame?
The answer to Question 1 is “never.” As other commenters have said, if you don’t like extreme results, then play with the low luck rules, or use a more conservative opening. It’s part of your responsibility as the player to select a strategy that maximizes your odds of winning, even including and allowing for the occasional “disaster” where you roll a 1-in-50 or 1-in-200 result that’s shockingly bad for you. Conservative strategies are slower and less likely to succeed, but they’re also less likely to trigger a disaster. You get to choose how much disaster you want to risk in order to further your strategy, and that’s a big part of what makes the game fun. If you change the rules to try to have your cake and eat it too by using an aggressive opening while artificially insulating yourself from the risks associated with that opening, then you’re removing one of the core dilemmas that makes the game great, and you probably won’t have as much fun.
The answer to Question 2 is “when the position is truly hopeless, or when all players cheerfully agree.” The mere fact that Germany doesn’t take Paris on G1 doesn’t automatically mean the Axis will lose – if you sent the Luftwaffe to sink both British fleets and succeeded in that mission, or if you successfully strafed Yugoslavia to setup a G2 attack on Russia, or if you captured Marseilles and sent some German naval units around the coast to get ready for an Afrika Korps strategy, then Germany still has some compensating advantages, and with a little luck and skill, you could still come out ahead. On the other hand, if you fail to take Paris, fail to sink the British fleet, and fail to weaken Yugoslavia, all in the same turn, then maybe the Axis really are doomed, and maybe it would be more fun to concede defeat, set the board back up again, and start a new game. Not every position is worth fighting to the bitter end, but many players are far too quick to give up. If you end the game whenever an unexpectedly bad result happens, then you’ll never get to enjoy any surprisingly unexpected positions.