What would cause a cow to not give milk after having a calf?

A cow SHOULD be producing milk after calving, since this is the kind of liquid that calves have to live off of for the next few months of their lives, or until they are weaned. All cows HAVE to produce milk after they've calved, no exceptions, no matter if they're a beef cow or a dairy cow.

However, a cow that is not producing milk after calving is a cow that could be malnourished (being too thin) and doesn't have the reserves to produce enough milk for her calf, or she's too fat, with too much fat deposits in the udder that are hindering milk production. Or, that cow is not being fed proper nutrition, and this is also causing her to not be lactating properly after birth. You will have to bottle-feed the calf until either the cow has been fed adequate nutrition enough to help her with proper milk production, or until he's old enough to be weaned while you put the cow on the cull list and give her a one-way ticket to the salebarn.