For anyone who has some real combat experience, breathing and punching come naturally. But when you asked them: when you throw your punches, do you inhale, exhale or hold your breath? Many don't know!
For those who are familiar with chi-kung, in particular chi-meditation, they will know chi will increase when inhaling and chi will be fortified when holding their breath. Chi tends to dissipate when exhaling, and it is through practice and good techniques that chi can stay level when exhaling. I shall go the last point later. Let's consider the punches first.
What is the answer? It is obvious, when chi is strongest, it is the time when your punch should be in contact with the body of your opponent. In short, it is when one holds one is holding one's breath.
When chi is strongest (holding one's breath), it is also the time when one better absorb punches, getting less injury. And it is also the reason why when a medical doctor pulls away the needle inserted on one's major vein on the neck (after major surgery), he will ask his patient to inhale, hold, and the he will pull out the needle. Likewise in doing external hard-chi-kung demonstration, the master will hold his breath when he is being hit at defined part of his body.
Finally coming back to the point of of keeping chi to stay level while inhaling, there is this "popular" advice of "squeeze your anus and hold your breath". This however can be achieved better by using one's stretched hands (in place of the anus). Through zhan zhuang practice, a practitioner can store his chi at his stretched hands while inhaling, and during exhaling (holding breath in incidental for this exposition) the stored chi will be used to fill up the body with chi (which will diminish in the exhaling process).
Reading up this point, alert readers will be able to speculate that other parts of the body (in addition to stretched hands and squeezed anus) can also act as reservoir of chi. And they are absolutely right!