When we do a kata with the Jo our Sensei has us count each movement loud. At first I thought it was a waste of energy coz I would get a heavy breathing faster. Now I realize that counting makes me breathe constantly, it is hard to talk without breathing.
Now if the series of punches you do is really fast I wouldn't raccommend counting each one of them, coz too fast might get you hyperventilating, but maybe counting every 2 or 3 punches according to the speed. Do this for quite sometime and then your body will get used to it naturally.
I have noticed for myself that when I stop breathing is coz I concentrate too much on the technique I am doing. Learning to breathe will get you less concentrated on what you are doing and more focused on the whole situation and furthermore will create less tewnsion in you, thing that in a real fight might save your butt.
Relax and breathe. Do not tie your breathing to your striking, I know many styles tell you to but I do not recommend it, if for no other reason than if you exhale and to strike and I see you doing that, I will attack right after your exhale (of course maybe that is just a CMA thing).
Relax, slow it down a bit and breathe. As you progress, pick up the pace, work on proper form and technique first and speed and power will follow. But if you do not breath you have no power and you will lose speed.
I have trouble as well. I find if I Aia too often I end up not breathing very deeply. I think it's due to tensing my diaphram. Anyways, I've temporarily stopped making noise when I punch and I am focusing on breathing like others have mentioned. Also, we do a wrestling drill where we start out on our knees and try to mount the opponent. Stikes and joint manipulation are not allowed. This has helped me focus on my breathing as well since we don't make stiking sounds during this drill.
Breath comfortably as you feel you need it. Go for a run and concentrate on breathing every three or four steps (or whatever timing your anatomy requires). Make it an unconcious reaction. Try training your wind more. If you can't breath you're probably too tense. Relax a little.
Watch boxers, when they punch they blow out so you can hear it, makes them breathe in too. Practice on the punch bags first, it becomes a habit very quickly and is carrid over into sparring.