Again, no one owns anyone. Never have understood that possession thing. It is common, but it isn't love.
Ownership has nothing to do with it.
It's about loyalty and commitment.
If I were in a long-distance committed relationship, such behavior would piss me off. And perhaps make me reassess whether we had a future. Maybe it was a one-time thing. Or maybe not.
But I think that if she's starting to edge herself out of the relationship, she probably won't be telling you anything more until she says good-by.
I'd have a talk with her about where the relationship is headed. A long, tough, honest conversation in which you might hear things you don't want to hear.