Should I bother or should I not? ladies?

I'd just casually ask her 2 more times about going on the date again before giving up. So the 1st one would be like a follow up to what you asked her "Have you seen my text about new year's eve?" then if you can follow it up eventually by "If you liked the first date, why don't we go (have dinner/movies/something) for another one on x day?"

2nd could be like "Let me know when you are free if you want to go out on a date again, we could do... (???)."

If you don't get a reply though I'd just move on. If she says yes then cancels last minute, I'd have to judge if you should drop it or not depending on her reasoning.

If you really like her, ask again as a reminder. If you give up, then let it go. Not sure why she hasn't answered you though, either she's easily distracted and forgetful (like me) or she isn't interested. It's one or the other. Girls have a bad habit of avoiding confrontation. So just go what you feel :D

I would suggest you to ask her in person if she say she's busy that means she is not interested and you should totally let go,but if she say yes then sure be my guest and go on and make your move.Hopes this help!

You can ask her but this smells of desperation. I vote to wait.

I think you should just let it go.

Find someone better for you :) someone who won't avoid you.

Yes, I think you should