Shit, I've been doing BJJ for a few years now, and I still gas in almost every class. It does get easier to deal with over time, but it's part of the sport.
There Will Be Gassage.
Some guys in my class roll a really fast pace (not spaz, just intense), and if I want to keep up and not get my guard passed, I have to match them, which is very tiring. I'm not the most athletic person, and I've had a few injuries which prevent me from doing a lot of running to improve my conditioning, so I gas faster than most of the guys in my class.
We usually get in four 5 minute rolls per class (sometimes more, sometimes less), and by the 4th roll, I'm usually gassed the fuck out. By this time I'm usually just holding on and just trying to survive. It does do good for my skills at escaping subs and positions though, because at that time I have no strength and explosiveness left in my tank to get out of positions/subs, so I have to work pure technique.
Cardio and conditioning is probably my biggest weakness in BJJ. I often get put in bad positions by guys who have less technique, but greater strength and conditioning. It sucks, but I just have to keep working at it.