Picking up girls in gyms feels like social circle game as we tend to run into gym members, at the gym.
I'm having a feeling that a part of her is attracted to you that's why she's receptive at the initial stage( exchanging numbers without you asking) and another part might be telling her that this is social circle and she shouldn't just fall in your frame of the seduction- that's why she might be holding back(flaked the first date and doesn't respond to grabbing drinks).
She's holding back by just giving you mixed signals because from the look of things she's into you because you confidently approached her.
I don't know how your interaction went with her. But she could sense that it might lead to the bedroom and is trying to slow things down.
After turning down two potential attempts to be with you she still smiles and is very receptive towards you.
Anyways, anything that has to do with social circle or groups where I'll likely meet up with members, weekly or daily- I just tend to be alot more ambiguous.
Everyone is subconsciously thinking about their reputation, especially women. Some women do have rules not to bang guyfriends from the gym or other meet-up groups because of their reputation.
If you can post a detailed interaction between both of you, I'm sure others might chime in with useful tips.