Pretty much any Company of Heroes skirmish as the Axis. For some reason, my allied AI would always get pubstomped about 20mins in by a huge Allied attack, while failing to deliver the same at any point of the game. One time, this happened while I was smashing through the enemy bases (4v4 map, all based lined up so I could flank all of them in sequence). I figured I'd have them, but the game didn't end when I took down the last HQ, and at that point the Axis base farthest from mine was gone, with each one moving towards mine being in gradually better (but still losing) states of assault. So, I run my forces back, and they hit this massive force that kills... I think all but half a squad of troops. I almost quit, but decided to wait it out, just to see what happened. After a VERY long span of pouring out all the reinforcements I could muster (thank gods for picking that command tree), the rush of Shermans and halftracks comes to an end. At this point, I have about half a barracks and armor factory (I forget what they're called, but it made the light armor), and a couple squads of engineers and one very experienced anti-tank squad.
So, now that I know *something* survived my earlier decimation, and they seem to have run out of forces, I queue up more engineers and send them to salvage whatever resources they can find in the tank graveyard that sits on my doorstep, while whatever soldiers I have go heal and reinforce and all that fun stuff. By now, I think the only AI that survived is the base next to me, and even then they're holding by a thread. It's at this time that I notice that the HQ foundations for my defeated allies still exists and have health bars. So I decide to send engineers to see if said HQs can be rebuilt (I didn't know it was possible at the time). Not only do I survive losing all my forces, and the brunt of four armies worth of troops, I manage to recover enough resources (at this point we had NO map control anywhere. Obvs.) from tank corpses to rebuild my base, and my allies were sitting on enough that, once their HQs were up, they were rebuilding in overtime; I could swear the AIs were angry from how fast they sent troops out to retake the map.
And what enemy structure survived all this carnage, you may ask, if you read any of this at all? A motherfucking machine gun nest. In the corner of the map. Pretty sure I firebombed it out of raeg.
A more recent 'Oh Shit' moment was a League of Legends match where my team was getting stomped on pretty hard. We get pushed into our base, down to the Nexus towers, and have little choice but to sit and push back the endless wave of super creeps while the enemy champs keep making (largely unsuccessful) incursions into our base. Most of my team wants to call it quits, but I notice that, each time the enemy attacks, we come out a little more ahead than before, and convince my team (Somehow) to keep going. I don't remember the team comps at all, but we reached the point that our sustained farming/line holding allowed us to fill out our builds, and give us the upper hand during the big fights. It was one of the longest games I think I've ever played, but we managed to turn it around.