What are some methods to show interest in a girl but also appear unavailable.

I ask this because there's a girl I'm trying to go on a date with, but we're rescheduling our date way too often in my opinion but I still think she's interested. Here's our attempt to schedule a date

1) I ask her for lunch on Friday - she's busy

2) I ask if she's free on Sunday instead - she's not since she's going on a vacation

3) She suggests dinner the following Saturday, a full week later, once she gets back into town - I accept

4) Couple of days before Saturday, she tells me that because plans changed she won't be back until Sunday morning and asks if we can reschedule to Sunday at 5pm (yea, she gave me a specific date and time)

Now I can accept this but should I? I don't want to appear too available but at the same time I'm tired of waiting and constantly rescheduling. What do you think? Is it worth it to tell her I'm busy or should I give her this one last chance and accept the offer?