Merchants won't make the decision about a card, other than to decline the sale if they don't get authorization from the credit card company. A site problem could possibly cause this, but they will correct that rather quickly.
Typically if wrong numbers get entered or wrong date or something like that, then an "authorization denied" will be given. That simply means that something is not recognized and the validity cannot be proven.
"Do Not Honor" is a response that is given when the card data is recognized, but the account has a severe problem such a being totally cut off, stolen, or something like that.