There's no doubt that WoW Arenas can be incredibly involving and intense, but there is something that can be very important to your team. Namely, cohesion and having the right mindset for battle.
Winning over and over again is quite the thrill, and gets extremely addictive. I'm sure thats why all of us play. Losing however, can cause a variety of problems. Just recently we've had one of our members get really pissed off about dropping a 25 point game due to a horrible decision the team made. The game was really ugly and there was no reason we should have lost but this is the power of an unorthodox matchup against many teams. Imagine a team with 2 mace warriors, a resto shaman, a moonkin and a paladin.
Our typical matrix is War/Pal/Pri/Rog/Mage, and we do the typical punish the cloth with expose/kidney nuking while the Mage cc's and tosses in damage. Against that team, we were genuinely confused as to who we should go for. All 5 of them are effectively in plate armor, so it hurts our strategy a lot and makes us grind it out, which is death against a double warrior team that never slows down.
Anyways, we lost, and after the game one of us blew up and started screaming and yelling about how stupid we were and how could we blow the game like that. All in all, I'd say it was called for, but the reaction afterwards was not productive. The best thing to do is to get right back up and play on like it never happened. Instead we bicked for a while about the strategy and then eventually the inital angry teammate logged, knocking us low for the night.
It is just a game, but it is also serious business. You want to be able to play competitively and excel. It is certainly demoralizing to lose, but it shouldn't stop you from playing. Learn from it and move on. Dwelling on it is going to hinder your progress from that game forward. Get angry, sure, but channel it in a healthy and natural way, namely absolutely crushing the next 5 teams to get even.
If you do get on a losing steak, maybe it is worth it to log for the night and get back with it the next day, but such occasions are rare, and really should be saved for fighting matrices that your group matches up very poorly against. (Even still, I would argue that the experience in playing them over and over is worth the loss in points, especially midseason after you have all the gear you need.) You do this to break the cycle and to break the concentration you have. Its much like a baseball game where the catcher calls time and goes to talk to the pitcher. The catcher isn't going to say anything that the pitcher doesn't already know, but the break in the action is all thats necessary to realign and refocus on the things you already do well. When you get into a certain mindset, as a pitcher, as a player, it can become self destructive. You start trying to force the ball in or trying to force a win through sloppy, but aggressive play. You do a lot more harm then good by playing on like this, but a short break can do a world of good.
Knowing when to keep going and when to break seperates good teams from great teams. It is important to recognize this in your teammates and also in yourself, although you probably won't be able to see it yourself. The absolutely last thing you should do, however, is log out pissed off while in the middle of a session because of one or two bad results. You hurt your teams progression, and you piss everyone off, making the entire venture not fun for anyone.