Well one of the problems with Sparring is that we get exhausted and things start to fall apart. Your hands drop, your sluggish, your winded and gasping for air. Well of course sparring more often can obviously help this. But you may not have enough of people to spar with or people that you feel comfortable sparring.
You can be extremely cardio fit and yet it taxes you to spar. Why? Well for one, your nerves may be up. And well again more sparring may help your nerves. The additional thing is that it's an uneven rhythm in your breathing. During normal cardio exercise you find a rhythm that matches your Oxygen need. If you are biking you will find a rhythm that is adequate for the speed and path you are riding on. Same for running etc..
As something changes.... your rhythm increases or decreases. But sparring is totally different. It's hard to predict when an attack will come. Or when an opening happens. The whole cardio aspect is random. Your body is constantly trying to adjust. Now add in the factor that when someone attacks you, that you may naturally gasp/hold your breath for that moment. Or you may hold your breath on your own attack. Again... it's hard to get your breathing to find a normal pace.
First.... you can train Cardio. Run. I know... people hate this... And well you will get more cardio fit but it will not simulate the actual act of sparring. One thing you can do is carry a jump rope over your shoulders... Run a distance.... Stop... Jump rope.... and then run again. Repeat. Want to add more into it.... Simply shadow box. This constantly is changing your pattern.. It conditions your body.
Want to throw the devil in the mix.... Do burpees in the mix of this. Burpees really change your breathing patterns. Do about 5/10/15/20 depending on your level. Try to aim for a number that really has you breathing extremely hard. Now follow it with Shadow boxing/footwork. Shadow box with foot work and with keeping your hands up and having good form. Concentrate on slowly your breathing and your heart rate.
If you really hate running... then just the act of shadow boxing with footwork mixed with burpees. Remember that after a set of burpees you want to try to calm your breathing and heart rate while shadow boxing. But when you hit burpees it's your burst. You want to explode. Go all out. Think of the burpees as when you actually have a confrontation in the middle of sparring. And then after the burst you want to regain your rhythm again.
Have another idea.... Shoot it by me... These are ideas that I have implemented and have worked. Bruce use to run the hills of his neighbor hood with his dog and follow it with a stationary bike or jumping rope.
Walk on... Wait.... SPAR ON!!!!!