I think the way my muscles relax is kind of how beef gets tenderised, a lot of beating 
On a more serious note i think you need to train for it in class, whatever technique you do you try and relax try and relax move fast relax, one thing i usually say is have you ever seen a horse or a sprinter run whilst tensing his mucles as much as he would do in a squat ? No exactly.
The more you train the more you relax, the more you relax the faster you move. So your body kind of says hey lets relax so im faster and dont get hit.
It might also be mental the fear of getting hit soyou tense and brace, just think of it as a game, its fun, so you play it dont worry bout getting hurt.
Also its good to learn how to tense at the last minute for example relax when hitting and boom tense the fist when it lands, this way you differentiate between relax and tense.
Also when being hit, you relax and get your partner to hit you lightly in the abs, at this point you expell all the air and tense the abs, but only at this point, this way again you learn to absorb the punishment, and you separate relaxation from tension, plus you wont have fear of being hit if thats what tenses you up.
As for sparring for over 15 mins thats a pros field !!! thats 5 3 min rounds or even a whole mma fight. Thats impressive !!!
I have the worst stamina so i cant even begin to comment on this. Unless you mean sparring in the sense of no contact just reflex training which is i do a move he does a move, in this case the easiest way is to pace yourself and play at your pace not the other guys.
About the chi kung comment i didnt quite understand it , if you can improve your stamina through chi kung thats great,by all means do it ! esp ifyou do chi kung before the match, you oxygenate thoroughly your muscles your blood stream etc have a ready supply so you wont run out of wind so fast.
Ive heard from pro’s that 800m is the equivalent of one round of a fight, so lets say you want to go 5 rounds as a goal, you would
start off with 800m jog with 1 min rest in between each round of 800m
once you are able to do this, you move on to adding sprints , so your programme ends up looking like
400m sprint 400m jog
rest 1 min
400m sprint 400m jog
rest 1 min
200m sprint 600m jog
rest 1 min
200m sprint 600m jog
rest 1 min
800m jog
etc ive seen this tailored in different ways for different amounts of rounds etc but 800m was the rule of thumb
Another way was for each round
8 x 100m sprints with 10-15 seconds rest per 100m sprint
and 1 min rest between each set of 8