A quick definition of continuing covenant:

A covenant is a formal agreement or promise between two parties. It can be a promise to do something or to refrain from doing something. There are different types of covenants, such as affirmative covenants that require a party to do something, negative covenants that require a party to refrain from doing something, and continuing covenants that require successive performance of acts. Covenants can be created by words of the parties or can be inferred from the whole agreement and the conduct of the parties. Some covenants run with the land, meaning they bind successor grantees indefinitely, while others are personal covenants that create a personal right or obligation enforceable only between the covenanting parties.