I've talked to my friends, but I'd appreciate anyone's opinion on this.

A little background: I met this girl through an old roommate last year. Thought she was cute at the time, but she was living in San Diego at the time and I am in San Francisco. Stayed in touch with her through e-mail, but figured nothing would ever develop other than a friendship.

Fast forward to this year. It turns out that she's moved to San Francisco for a year working with a non-profit. I took her out a couple times last September and things seemed to be going really well. I was enjoying getting to know her and trying to take it slowly but steadily.

It's been two months since we've actually seen each other, though we've kept in touch through the phone, texting, and online chats. However, this whole time I feel like there's been some awkwardness building up (possibly stemming from anxiety over wanting to hang again, yet not having time due to one thing or another coming up that's ruined each of the previous opportunities we've had to do something). I feel it getting a lot harder to contact her than it used to be.

This last week was particularly bad. She used to be regular about getting back to me (even to say she was busy - which I understand... we all have lives), a text message on Monday asking if she was free to hang out wasn't responded to. Than, I saw her online a couple days later and tried to initiate a chat with a simple "how's your week been?"... didn't get a response to that either.

I'll give the benefit of the doubt and allow for the possibility that she's just been busy. But I also think that I might have been a little too aggressive in trying to see if anything could develop. I'm backing off for the moment and giving her space, hoping she'll get back at some point, but do you all think I'm out of luck?

I don't see proof that you are out of luck, or a lot of evidence, not yet anyway. She may have met someone and is seeing how that goes. She may be making family holiday plans. She may be worried about work or end-of-the-year busy at work. There's even a possibility that you aren't the man for her and it's taken her this long to realize it, and she doesn't want to hurt you. And finally (of course there are many others) is there a chance that she thinks you aren't moving along to the next stage quickly enough rather than too fast? Have you been too casual for too long about 'just hangin' when she wants to be asked out on a real romantic date?
I have no idea; those are just suggestions.

I think you should stop and let her respond to you now because this is what you have quoted:
"a text message on Monday asking if she was free to hang out wasn't responded to. Than, I saw her online a couple days later and tried to initiate a chat with a simple "how's your week been?"....didn't get a response to that either"
The ball is in her court to act now and maybe you were to aggressive with her? Who knows except her, you could send her one last message or text but is she doesn't reply then move on and try to meet someone else! Good luck!