Recently I was listening to the radio and the host used some expression (that now evades me) to explain that the song 7 Years by Lukas Graham quickly becomes uninteresting to listeners after a few plays - in other words the first few times you hear the song it is interesting but after that it becomes less interesting, compared to some songs that the user enjoys listening to over and over again.
I seem to recall that he used the word burn .e.g. the song's 'burn rate' however googling that only brings up references to a companies burn rate (the rate that it looses money), but not a song's.
So my question is just that, what is the term for this?
I think your best bet is to say that the song has been overplayed on the radio (or in other words, an overplayed song). While I don't consider Urban Dictionary to be a reputable source when it comes to definitions, the one they have posted certainly fits the use of the term:
used to describe a hit song that is played on the radio (in stores, on the internet, on iTunes, at parties, etc.) numerous times to the point of annoyance
Dictionary.com says that this is "a tune or part of a song that repeats in one’s mind"; and this is often used in a context where the song is considered highly annoying. You can easily get tired of something annoying.
Or, there is the word "passé" which Dictionary.com says means "no longer fashionable"; this can also refer to songs, and unfashionable songs soon grow tiresome.