I rarely approach the female half of an obvious couple unless I've been encouraged to do so by the guy. I even notice if two people walk into the room together. To my way of thinking, it shows that I respect the fact that they ARE a couple.
I'm hardly a conservative person. I'm not big on tradition, couples "owning" each other, or even codes of tango unrelated to maintaining the line of dance. Yet I do everything you wrote, because people who attend the milonga together often have plans, and it isn't my place to mess with those plans.
For instance, I went out the other evening with an out-of-town tanguera who isn't my life partner (my life partner wasn't available). We had this crazy idea to dance particular orquestas in specific ways to see if we could do it. Had someone horned in, that would've thrown our plans. It wasn't important that we weren't a "real life" couple; it was important that people let us alone.
Also, it's possible that your GF has gotten too good for some guys to think that she would enjoy dancing with them, especially if you two look really good dancing together.
Intimidation is a real thing in tango. There are followers I don't invite because they dance exclusively with leaders who teach, perform, and tour. I cannot give them a tanda that good.
Your point about "look really good dancing together" is huge, too . . . two "5 out of 10" dancers can look like a couple of "8 out of 10" dancers if they're extremely familiar with each other, because they have a lot of secret codes and error-correction going on, not to mention great comfort with one another. That, too, can intimidate.
Another thing I always notice about the women is what movements they seem to enjoy while dancing. If those things aren't in my preferred vocabulary, they most likely won't get an ask from me.
For me it's less about movements and more about style, particularly embrace. I embrace close and low, and put the point of contact closer to the belly than the chest. I keep my sacrum straight down under my cranium, and want my partner to do the same. I lead everything through torso deflection, dissociation; I refuse to "drive" the dance with big steps around my partner, or to add "oomph" with the arms. So, if I see a dancer who responds to that, I'll invite them; if I see one who insists on a high embrace, outthrust rear-end, exaggerated leader energy, etc., I'll pass forever.
And, yeah, first refusal is last refusal for me.
At least that evening, probably that month, maybe that season, and conceivably forever, depending on how the refusal felt.