In Das Rheingold, the Rhinemaidens lose the gold (the verb is problematic). In Gotterdammerung, the rope snaps and the Norns lose their eternal wisdom. In both cases the sisters have an object which, at the end of the scene, they don't have. In the case of the Rhinemaidens' loss Alberich clearly has a causal role. The Norns' recount the story of the previous three evenings, and whilst the rope snaps when they recall Alberich's actions the music is most certainly Siegfried's.
The Valkyries stand apart in two ways. The scene starts with all the Valkyries except Brunnhilde. In contrast to the Rhinemaidens and the Norns, Brunnhilde brings an object to the group. The rejection of Sieglinde is quite distinct from the loss, but by rejecting her the sorority, in turn, loses one of its own members. Each group of sisters loses something, and in this respect, the structure is of loss from the outside.
There is, here, no 'meaning'. One could construct or project onto these events a feminist interpretation but that would not be in this pattern. There is nothing outside of the pattern. There is nothing except the pattern.