Is it valid to swear or take an oath to stop thinking about something, even if this thought continues after paying the expiation for breaking the oath, or must the oath be renewed after each breach?

The fundamental principle is that an oath is dissolved by the first instance of breaking it, and the one who swore the oath is not obligated to repeat the expiation (kaffara) with repeated instances of breaking it, unless the wording of their oath necessitates repetition, or they intended it, or custom dictates it. The mentioned wording indicates an intention for repeated breaking of the oath, thus expiation is required each time it is broken.