Vary your intensity: Your first day sparring in Jiu jitsu was probably pretty similar to mine and everyone else reading this post – you locked up with your opponent and gave everything you had at maximum power until you quickly exhausted yourself and got finished. The path towards expertise is largely bound up with PACE and INTENSITY. It doesn't matter how well conditioned you are – if you go at maximum intensity for a length of time, you get exhausted. The key is to understand that high intensity is only required for brief periods in Jiu jitsu, usually when either or defending a potential or submission. This is only a tiny fraction of the total time of any given match. The rest of the time you should be a state of relatively relaxed, but alert, calm. Learning to cycle between long stretches of calm and short bursts of high intensity effort is a huge part of your and is the true key to endurance on the mat. The you get at this , the longer you can and the fewer injuries you will suffer. In addition your sparring will become more enjoyable as a side benefit. If you have a hard time playing calm, make a note to stop in certain positions where you feel you can recharge and compose yourself, then as you improve, stretch those positions out more and employ more positions. Make it your goal to spend 70-80% of a match in a fairly calm state so you can save yourself for the 5-10% where the match is won and lost.