I know how you feel, unless carefully balanced (such as Sora's first fight against Squall in KH1) it tends to break the game's immersion when there is e.g: any enemy who just never runs out of HP and/or blocks all your attacks (e.g: Kevin vs. Karl in SD3, Dart vs. Lloyd in Legend of Dragoon disk 1, Terra vs. Phunbaba in FF6), or an obviously uber-tough enemy who wipes you out in a single turn and there's nothing you can do about it. (Though in their defense, the latter is actually less annoying than the former.)
Oh god, Roy Mustang and Alex Louise Armstrong at the end of some such Full Metal Alchemist game. I fought them for like two hours straight and eventually ran out of healing items. I just wanted to see how far I could go before I inevitably lost. I sure gave 'em a run for their money, though, they actually started fighting harder after a while. 8)
Dunno if it's been said already, but Ghaleon from Lunar: Silver Star Story Complete... took me FOREVERZ to beat him. xD
Though I was young then. Maybe he's easier now. =O
There's one boss battle in Tales of Destiny that sorta works like that... You're supposed to lose during the first fight with Leon to continue the story, but if you DO manage to beat him you get an alternate ending of sorts and the credits roll.I want to see a boss battle in a game where there are both win and lose scenarios, however if you didn't make some kind of progress during the battle (i.e: if you just stand there and let yourself get killed) then you still get a "Game Over".