They can, but only if they are dividends on preferred shares. The nature of a common stock dividend payment is that it is not required. Dividend payments are a byproduct of net income. They are one option, among many, that a company may use to allocate its profits.
For example, a relatively young startup company may be growing quickly and generating significant profits. However, instead of issuing a dividend, they may choose to put the money that would have been used for dividends into operational improvements to enhance efficiency and create further growth. Contrast that with a blue-chip company that may choose to allocate a portion of their profits to pay a dividend. Both companies may be exceptional companies, but for different reasons, they are choosing to allocate their resources in different ways. The extent to which one option is seen as better than another is from the perspective of the investor and what their objective is for owning the stock.
It should be noted that once a company starts to issue dividends, they will typically make a strong effort to continue to issue them. If the company is having profitability or cash flow concerns they may reduce the amount of the announced dividend, but they will generally go to great lengths to ensure the dividend is paid. Preferred dividends are different in that they must be paid and therefore they do reduce net income. Preferred dividend payments are also used in the calculation for earnings per share (see below).
If a company does not issue a dividend, then their net income should be equal to the difference between their retained earnings from one quarter to another.