Is an oath that requires repetition dissolved upon the first breach, such as one who swore "By God, every time I pass by you, I will greet you," by analogy with the Hanbali view that if one breaches some of multiple oaths, only one expiation is due, and the remaining oaths are dissolved?

What you mentioned—that the Hanbalis believe that if someone takes multiple oaths on multiple matters, such as saying: "By Allah, I will not eat; by Allah, I will not drink; by Allah, I will not wear," and then breaks some of them, only one expiation (kaffarah (definition)) is required, and the other oaths are dissolved—is not an accurate statement.

The Hanbalis hold that if the oaths pertain to different categories, as in the example given, the oath does not dissolve by breaking one of them. So, if he breaks one, an expiation is required of him. If he pays it and then breaks another oath, another expiation is required of him. If he breaks all of them before paying expiation, then an expiation is due for each oath, and this is the view of the majority of scholars.

As for the statement: "By Allah, I will not eat, nor drink, nor wear," this constitutes a single oath covering different categories. If he breaks one of them, only one expiation is required, and the oath is dissolved.

The particle "كلما" (whenever) denotes repetition. So, if he swears: "By Allah, whenever I pass by you, I will greet you," and he fails to greet each time, if the breach of oath recurs before expiation, a single expiation suffices. However, if he breaks the oath after expiation, another expiation is required of him.