Is there a technical term for someone being burnt out on something they enjoy?
There is no specific term for this entire phenomenon because there is more than one psychological theory playing a role in your overindulgence or "binge". Fatigue from repetitiveness, durability bias, and habituation all play a huge role in determining how long you can listen to a certain song before its gets repetitive and boring. 
On the other hand, tolerance from substance abuse has its own special term: Drug Habituation.
You would be best off searching scholarly journals using the keywords fatigue and habituation.

Further Reading:

https://en.wikipedia.org/wiki/Habituation
http://changingminds.org/explanations/theories/durability_bias.htm