This kind of stuff is entirely normal, and does not mean that she's immature,... In fact she correctly identified the problem: after spending a while together, a relationship either becomes deeper, or it starts to have problems, if this is not possible, because the status quo is not satisfactory anymore.

I think your best bet is to totally change the context of your relation. Right now you are very defensive (which is normal), but that is not very pleasant, and does not encourage a come back. A better approach is to refrain from putting pressure in her, and on the contrary think about new ways of spending some good time with her (by doing other activities, etc). She must understand that she has not exhausted the interesting stuff to do with you, that you can maintain her interest. If she does not want at all to spend time with you, then just think about new ways of spending time with common friends.

I think she's afraid that she will be always stuck in the same kind of relationship, and it would be best if you show her that your relationship can evolve, and cater for new needs as they arise.

And trust me, this kind of crisis will repeat themselves each time a relationship goes to the next level (deepens), so you'd better learn how to deal with it, because it will be the same with any woman you go out with.