I would throw in the towel myself, but I'll proceed under the assumption you'd rather not, or else you would have already.
You could confront G about your perception that it's not "I'm not in the mood" but rather "I don't want it with you." To be the Devil's advocate, it's conceivable that she hasn't been in the mood at all and that S has been pressuring her anyway. But more likely, something happened during one of the threesomes that made her feel weird, and now she doesn't want to do that anymore, but she's too chicken-shit to tell you about it and work it out.
Or maybe she was bi-curious and now that her curiosity's been satisfied, she realizes she's not really down with pussy.
I guess my question to you is, what's in it for you? What outcome would you like to see? Perhaps you would feel better if you had more of a say in how the relationship works, e.g. having sex with S without G needing to be present.
Incidentally, this whole poly thing also means you're allowed to have relationships with other people outside this couple. There's no reason that just because they're not meeting your needs, you can't get your needs met with someone else. Unless of course, that's another one of "their rules" in which case forget 'em and move on. They don't own you.
Gralson: my husband (works out of town).
Auto: my girlfriend (lives with her husband Zoffee).
The most dangerous phrase in the English language is "we've always done it this way."