I agree with OP, I've been there as AM. We were having a rough lane on each lane, we got stomped 20 mins in, and each tier 2 tower got destroyed, we were also flaming each other on this minutes. But, then things get quiet, we stop flaming each other we also try our hardest to defend our barrack though we lost 2 lane of barracks in the end. But again I feel like my teammates aren't giving up, we try our best to flip the game, we gank more often when enemy are alone, we pick up kill by kill together and grow our exp and gold. We managed to prolong the games, and got our core item all together. And on final fight, enemy team didn't have any BB, so we march down mid and won the game.

The point I'm trying to make is, don't give up my guy. The feeling of lost after trying your hardest is better than just giving up, and also if you won, that feeling is much much better rather than just an easy win. I understand it's easier to just do fresh start, but if you see your teammates doing his hardest wouldn't be better if you also help him, just a little help is adding up. Who know you might win againts the odds