Why did Yukine stop stinging Yato?
well, he basically learned his lesson; his character changed a lot after the whole incident (Hiyori helping him afterwards is a big reason too); He is, afterall a teenage boy~

if he would continue to "sting" Yato... [Spoilers avoided] (you should see season 2 if you haven't already, since it covers that in the anime with Bishamon)