The description for Luring Song in the Harpy's statblock in the Monster Manual, page 181, reads:
Luring Song. The harpy sings a magical melody. Every humanoid and giant within 300 feet of the harpy that can hear the song must succeed on a DC 11 Wisdom saving throw or be charmed until the song ends. The harpy must take a bonus action on its subsequent turns to continue singing. It can stop singing at any time. The song ends if the harpy is incapacitated.
While charmed by the harpy, a target is incapacitated and ignores the songs of other harpies. If the charmed target is more than 5 feet away from the harpy, the target must move on its turn toward the harpy by the most direct route. It doesn't avoid opportunity attacks, but before moving into damaging terrain, such as lava or a pit, and whenever it takes damage from a source other than the harpy, a target can repeat the saving throw. A creature can also repeat the saving throw at the end of each of its turns. If a creature's saving throw is successful, the effect ends on it.
A target that successfully saves is immune to this harpy's song for the next 24 hours.
So as far as I read it, the condition ends when the save is succeeded or the song ends. If an affected character is deafened or moves through the area of a silence spell, the song still continues. But it seems only logical to me, that upon ceasing to hear the song, that this would have some effect. So am I correct in reading that RAW the effect would still continue for a deafened character?