Is it okay for a girl to ask a guy out, more than once?

Nope, the cap is set at one time per person per lifetime. So, this time was wasted (as girl was wasted at the time of asking). It is sad that it happened but there is a national registry for such metrics, and this girl is in it already - I just checked. And I am typing all this to tell you just how ridiculous you sound.

There's nothing *wrong* with it, but I wouldn't do it.  He knows you are interested.  The ball is in his court, so to speak.  If I really liked him and thought he might like me too but is just really hesitant, I would say in a lighthearted way, "Hey, remember that time I was drunk and asked you out?  Why didn't you say yes?"  (Punch playfully in the arm.)  "Do you not find me attractive?"  Then he is free to say, "No, it's just that you were drunk and I wasn't sure you meant it," or, "Yes, you're attractive, but I don't like you in that way," or, "Hell yeah, I think you are attractive.  I've been kicking myself ever since for turning you down." His response will give you a good indication of whether it's worth a shot to ask him again.

Yes, it is OK. But if he was turned off by your drinking, then be prepared for a no answer. Men might sleep with girls who get drunk, but they usually do not want to take them home to meet their mother. Be more discriminative in your drinking.

Yes. I don't like that the girl is drunk here. Aside from that, she is doing it right. If you want something, you have to kill for it. Slay the guy if that's neccessary. Whatever it takes until he's yours. But you may find he isn't what he looked like before.

The girl ought to ask him out when he is drunk this time.  If he seems cool while drunk, then she ought to ask again when both are sober just in case his coolness was a fluke.

Sure it's OK, but I've never done it. Before I married, it was always my personal policy to ask a guy out 1st if I liked him but he'd not asked me, but the 2nd date was up to him to propose. I did that so I could quickly know whether he was truly interested.

This all depends heavily on what is mean by "it did not go down well." Why didn't it go down well? Once you have answered that, whether she should try again will probably be obvious.

We live in a liberal society. If a girl is asking out a guy, without any hideous intentions to kick his butt in the future then I think it is pretty much acceptable to approach your dream guy again. Remember No trend is trend unless someone sets it. Go for it girl, Be brave.:)