“Until the song ends” is a bit unclear
The wording here gives us less than what we’d really to have for a clear ruling. The Luring Song plainly states that as long as you can hear it, you are susceptible and that it continues until the song stops.
Adding silence into the scenario presents us with a difficult set of options. On one hand, it makes perfect logical sense that if the area is under silence, then no song is heard. But what happens? The Luring Song isn’t clear about that situation, so that leaves the DM with some options.
I hear nothing!
A DM could very reasonably rule that an unheard song is a stopped song. Whether or not it means it’s temporary or if they can be lured again would be up to the DM as well.
The power is in sustaining the song
The language also isn’t clear in how the song’s power is really used. A DM could also very easily rule that once under the sway, the only ways to end it are the actual singing stopping or the harpy being incapacitated. We can have all sorts of fluff as to why that still works, but it’s magic is always a solid option, but if you want more you can look at this as as parallel to concentration mechanics where as long as the harpy is singing, the song’s effects continue.
Go with what goes well at the table
Ultimately, these decisions come down to what works narratively and thematically at the table. What tells a more interesting story for you and your players? That’s the question you’ll need to ask yourself here.