Here's what she's saying, IMHO. She thinks she might want you, but isn't all that sure and wants to keep you there in case she decides she does want you, or if nothing that appeals to her more comes along soon. She actually would like you to move near her, except if she decides she doesn't want you anymore it's a sticky embarrassing situation and she couldn't easily be done with the relationship.
Move on. This is not going to get better. People in a relationship who "need space" aren't suited for the other partner who doesn't "need space", i.e., less of the relationship.
Hi there. My suggestion is to take this at face value for now. Some people ARE like turtles when stressed. They pull themselves into their shell to 'deal'. I am a bit like that. Your response to her when she says she is stressed at work is to look at it like an excuse for not being with you or around you or calling/texting you rather than "oh my gosh, I'm so sorry I've been adding to your stress. Take the time you need and I'm here for you." She's saying she's going through a difficult time and you still made it all about you and your feelings. You still are today.
I'm a married woman. When my husband has an issue that is weighing heavily on his mind, I can always tell. He starts off with a bit of distance, doing his own thing around the house and not wanting to 'let me in' right away. I just give him his time and then he opens up to me. If I told him when he did that that it wasn't okay to need his space . . . it totally takes away from what HE is going through. Do I think my spouse doesn't love me because this is his way of dealing with something emotionally (or otherwise) hard for him? I try to be open to his style and there for him. I don't take it personally and try to give him what he needs.
So, your girlfriend is telling you that times are difficult for her and she's trying to cope and the pressure this relationship puts on her and her feelings that she has to please YOU when she's just trying to get through the day . . . think about that.
Unless you think it is all an excuse which that does happen.
So, give her space. TRY to be understanding and make this about her and not you and your hurt feelings. You can decide for how long you want to do this. If you get to the point that it seems pointless, then you can tell her that this isn't working for you and move on. And as your relationship gets closer (as in you two are true partners rather than long distance lovers)-- you can tell her that you want to be there for the good, bad and the ugly. That you can give her space to lick her wounds but you want to be there for her too. Etc.
But clinging more to a relationship where someone is clearly in a different head space than you doesn't work to fix it. I'm sorry. I do hope it works out for you and please come back and let us know!
Don't change your life plans for this relationship. She's telling you that she is busy w/her life. Appreciate what you've had w/ her, and make a new path in your life. Good Luck :)
You can test the situation easily enough. I believe she is finding work stressful. The question is what else is going on.
Either
#1 she is finding her work stressful and has also found someone new, or
#2 she is finding her work stressful and is not that into you any more without finding someone new, or
#3 she is finding work stressful and would welcome more of you.
Test this by asking her to marry you.
If she says yes, then it's #3. Plan to have her move to your town where the cost of living is less.
If she still says she needs space, it's probably #1.