I'm looking at your post... and then I'm looking at the majority of the responses, and it looks like most of these guys have NO idea about what the man's part of an interaction is supposed to be. So, let's look at your post again, and see where (a) you're screwing up, and (b) misreading her interest:
"I started seeing a new girl a few weeks ago. She works a demanding job, but everytime we chat all I hear is she is exhausted or so busy. Last time we met she was initiating kino and told me to call her. That was the weekend before the past weekend. Now she rarely initiates conversation."
Were you just calling her to chit-chat? No bueno. The goal of getting a girl on the phone is to ask her for the DATE. You don't start doing "chatty" conversations until you're the boyfriend, and even then you (a) keep it to a minimum, and (b) save the majority of interactions for when she's there with you in person.
Also: the reason she's not initiating as much conversation is because - wait for it, wait for it... IT'S THE GUY'S JOB TO INITIATE PHONE CONVERSATION, especially as it pertains to asking her out. Yes, she could like you all day, but at some point most girls start to realize they're doing most of the contacting, which doesn't make them feel like the guy that likes them is doing enough to show he likes her. So, they'll dial back their contact initiation to see if he does it. Yes, it's a test and it sucks, but in reality YOU should be the one doing most of the contacting in the first place!
"I told her I wanted to get together soon to let me know when she was free - that was 10 days ago. She seemed really excited."
Weak. You basically said: "So, anytime you wanna go out, I'll be available and ready to jump at the chance to do so because I have no life of my own." At least that's what it comes across as. Furthermore, you saying this means, in her mind at least, that you have NO actual plans for what you'd be trying to do were she free, nor have you tried putting any thought into it.
Here's something you, and the rest of the guys here, need to understand: if a woman likes you, she will MAKE time to do activities with you... IF you have a plan of what you want to do. If you hit her up with the ol' "lemme know when you're free so we can do something" routine, what does she have to get excited about? The prospect of seeing you? HA! That's your ego - what actual activity should she be looking forward to? A dinner? A play? Skydiving? Bowling? You don't know, therefore she doesn't know, therefore she's not calling you up when she has a free day!
So, what do you do? Wait a few days, then call her up and say "Hey, there's a new restaurant in town (find one), and I wanted to take you there and try it out. My schedule is a bit busy this week, but I do have Thursday and Sunday available, what would work best for you?" I don't care how busy she is, she's got to eat at some point, right? If she likes you, she'll either pick one of those days or give you an alternative day; if she doesn't, she'll continue to be busy and not give you a counter-offer.
Geez, people, don't make this as hard as it has to be!