I was ignoring this discussion for some time, but since accusations were tossed at the 5000-win streak's legimitacy, I suppose I have to step in for a word.
I've definitely had luck with that streak - the close battles I've posted demonstrate that with the near-loss at #3186 and others, but there are also some that I haven't posted as much about (outside the IRC channel), including:
-A very nearly lost battle in the 4500s with Greninja/Charizard V5 against Veteran Saba/Isabella with Heatran3 (Solar Beam), Terrakion2 and other top threats showing up. I played horribly, losing Gastrodon and Entei to Heatran3 and Terrakion2, respectively - then misreading calcs with Aegislash to get it killed as well. With three Pokémon dead for nothing, the battle ended in a 2v3 situation with MegaZard and Latios facing off against Heatran3, Entei2 and Terrakion2 (locked into Stone Edge) - and the only reason I was able to win in such a sure-loss situation was that Latios succesfully protected twice in a row while Entei1 used Will-O-Wisp on Terrakion (which failed to KO Latios and eventually struggled to death thanks to the burn) and opted to waste time instead of boosting with Calm Mind, and Heatran3 not having Flash Fire which I knew from it not having switched in after using Flamethrower earlier on Turn 1. If it did have Flash Fire, the battle would have proceeded differently because of the switch and it probably wouldn't have ended like this. It was after this battle that I switched Latios for Infernape to better handle Heatran and having access to Fake Out.
Anyway, I thought I had lost the battle for sure when Zard+Latios were against three enemies - but thanks to great luck, the win happened against all odds.
-The Rasmus battle with Mega Gardevoir where Garchomp3 dodged stuff and crit things with Outrage that I mentioned briefly (and forgot to save the battle video for) - I won it, but the AI's backups being Ferrothorn and Gastrodon instead of something threatening were crucial, and with one more 25% evasion roll, it might've easily been a loss.
-Miscallenous freezes with Lucario/Greninja and Mega Gardevoir - as the teams have a lot of Ice resistance and little Ice weakness, it isn't very common, but Rotom-W has gotten frozen by Blizzard many times, as have Lucario and Gardevoir. While there's been no outrageously close battles resulting from a freeze that I can recall, it's definitely a factor that can and will blow a battle wide open against threatening opponents.
-One time, I saw Glaceon1 (Quick Claw) in the center getting two Helping Hand boosts from the sides... and using Protect (without a Quick Claw activation). While this is a pretty ridiculous scenario as not many Eeveelutions have Helping Hand, if it did use Blizzard and activate Quick Claw, it could have OHKOed Lucario through resist and have a good shot at freezing other team members - and survive to use another Blizzard on the next turn, too. I wonder why it didn't go for Blizzard as with two Helping Hands, as it would've KO'd Greninja and Lucario - my best guess that the AI's move selection doesn't take the Helping Hand boost into account, or it doesn't know that its allies are going for it (which seems likely since Helping Hand into a status move is not an uncommon play from it).
And there's more. As
faith_grins said, no matter what team you use, there'll always be a combination of misplays and hax that will take you down, though some teams are more resilient to it than others. I'd credit the many Ice resistances that Lucario/Greninja has for the relatively low impact that freezes have on that team, for example. Greninja/Charizard has Sunny weather preventing freezing. And on the new Doubles team, Gastrodon has Scald and Talonflame has Flare Blitz to thaw out, which have both been used to do so during the streak - quite often for Gastrodon, for that matter, as the inability to use Water moves drives Water-types with Water/Ice coverage to use a low-damage Ice Beam repeatedly.