I disagree as with the case I linked. What about BTK? I am sure there are more..
There was lapses between successful killing but not in his behavior, really.
He stalked his victims for a long time. Some of them caught him and filed restraining orders orders and at least one got away. He was still obsessed but forced to lay low, so he would go back to taunting the public with deliveries and clues.
In his confession Rader said during the gap between '77 and '85, one victim got away and made him so mad he obsessed for a while. There were 2 others in the early 80s. Then the gap between '85 and '91 he admitted admitted to stalking one woman. Of these 3 women, 2 filed restraining orders and one moved away and he didn't follow.
So the behavior didn't stop, it just wasn't successful all the time. But he ways had a thrill to go back to in the ebbs.