NO WAY! My crush/girlfriend/notreallysure has depression and anxiety and we've been sorta dating for a few weeks now, but recently she has been brushing off my conversations with her, she never truly answers when I ask how she is, she won't talk about her feelings with me, but I am her for her and I want to let her know that? I have told her that I will be there for her but she still won't talk about how she feels. But I'm not going to leave her. Her anxiety tells her otherwise and because of this she tries to break it off with me sometimes when she is feeling really low, mainly because she doesn't want to hurt me with her emotional state. but I wouldn't leave her.
That depends on the situation option sounded sketchy so I pretended it didn't exist.
If, however, the situation is that you're not actually into her, then you should leave her but do so carefully and remain a very very close friend, also ensure that she talks to you about how she is feeling.
If she's a girlfriend, most of the time I would say no. But it depends on the situation. If she was my wife, then absolutely NOT!!! I would never leave my wife. I take "in sickness and in health" very seriously. This includes depression.