Should I still persist on approaching a women who stood me up on a first hangout or we can say first date?

You're right, you should have got her number...she might have gotten the time wrong or something might have come up. Some people have facebook that the never check, so she may not have gotten the message. I say, if you happen to run into her again, you should ask her what happened, then ask her if she'd like to reschedule, then get her number and call and confirm the night before (and give her yours, too!) If it happens again, or she gives you some wishy-washy answer like "ohh, I forgot" then don't pursue it any further.