My interpretation of this is that RAW does in fact support the charm falling off of a character that can no longer hear the song (for any reason, but perhaps especially a Silence spell).
My reasoning is that Luring Song simply states that it's effects end when the song ends. The first thing we need to do is define what "the song" is. I have seen plenty people make the mistake of equating "the song" with "the harpy singing", but logically these are not the same things.
The "song" is produced by the harpy singing, yes, but functionally these are separate events or entities. The song can only exist through the harpy singing it into existence in the first place, but once it exists, it exists independently of the harpy that created it. That is to say that it's existence (as an object or an event) once it's been sung is no longer dependent upon anything the harpy is or does. So, what is "the song". Well, common sense (which D&D often requires us to use - gravity for example, is presumed to exist even if it's never explicitly stated - in a fantasy world it is presumed that everything works just like it does in the real world, except where explicitly stated otherwise, for example magic) tells us that the "song" is sound. That is, it is composed of sound (just like words or any kind of utterance from the throats of creatures is). A song, by definition, is composed of sound.
That is to say, it is not composed of light, or butter, or dragon scales, or fire, or necrosis, negative or positive energy. The song is "made of" sound. That's what it IS. It is sound. Magical, yes, but still sound. It's constituent parts are of sound.
Now, the Silence spell says that no sound can enter and no sound can be produced inside the zone of Silence. This is equivalent to the song 'ending' inside the sphere, because 'stopping all sound' is grammatically equivalent to "ending all sound". In other words, if all sound dies within or at the boundary of (for sounds aimed at the sphere from outside) the sphere of Silence, then that sound "ends" right there (at the boundary if it's external, or inside it if not).
Therefore, the sphere of the Silence spell causes sound to end. It causes the Luring Song to end. The song ends, at the boundary of the sphere, or never even gets created if you put the spell on top of the harpy. Silence ends sound, therefore it also ends anything that is sound based, which would include things like Bardic Inspiration as well as Luring Song.
This means that you can stop a harpy both by casting it on top of yourself (just be careful not to silence your own casters), OR by casting it on the harpy which stops her from singing (but doesn't stop her from leaving the area of Silence).