I would say it is used in the singular most often. In the singular, it refers more to the CONCEPT of profit (revenue - cost). The company made a profit this year; it did not go deeper in debt. In the plural, it is referring to many instances of making profit, for example, the profits from all of its 100 stores.

I agree that the usage here may seem a little irregular. It may not be possible to give an easy rule but this may help a little: a) Singular when talking about the overall performance of a business e.g. Last year XYZ Ltd made a (big) profit (rather than a loss). b) Plural when talking about the profit made on a group of individual transactions e.g. Market traders made profits yesterday of 10% more than the previous Friday.