As PPs have said, you are not her minister. She certainly sounds as though she needs a level of support and counseling that one person cannot accommodate on their own. I have a friend like this, too, and I sympathize. It feels like you're being a "bad friend" to distance yourself, but you need to take care of yourself!
I realized things were out of control the second time my friend called me and left a message insinuating she was suicidal. The first time she said "I wouldn't hurt myself but I'm scared because right now I really want to." I rushed over, scooped her up, and moved her into my home for awhile (her living conditions were a big part of the problem). In retrospect that was the wrong move. She stayed with us for about 6 weeks while she got her life straightened out and got into a better living situation. Then a couple of weeks after she'd moved out she messaged again, this time saying "I'm freaking out because I have that feeling again, like before I came to stay with you. Please call me!!" I knew she was hoping I'd invite her to come back but that wasn't going to happen. I'd been friends with her for probably 3 years prior to this and she'd never made that kind of statement before so I realized that she'd discovered a trump card, so to speak, and would probably begin to play it often. I have a husband and three children and she simply cannot be the center of my attention. Instead of calling her back I texted and said "Bad reception, can't call. You need to call 911 or go to the hospital and have yourself admitted right now!!" I basically called her bluff and I was right because she replied "I'm not THAT bad, just feeling down. I don't have anybody but you.". Obviously this couldn't go on. I could not be responsible for whether she sank or swam, you know?
What I did was slowly pull back. I didn't think a sudden cut-off was the best move because it would have been Major Bad Drama which she would have used for a giant "woe is me" pity party with our mutual friends, likely complete with threats of suicide, and I didn't want to deal with that. Also we DID have a lot of fun together sometimes. I didn't want to cut her off, I just needed to get her to stop leaning on me so heavily. So I'd ignore her texts and emails for a few hours (after a while I upped it to a few days) and then reply with something short like "I'm sorry I wasn't able to get back to you sooner. I hope you're feeling better!" I basically derailed the attention train. We still communicate on facebook but she hasn't contacted me regarding an illness, fight with a relative, etc. in a long time. I'm sure she still needs that attention but she must be getting it from someone else.
Your situation is a bit different since you really have no friendship with this woman other than you being her support system. You could absolutely give her a full cut right now, but if that bothers you, I think you should say something like "Friend, I wanted to give you a heads-up that I'll be mostly out of touch for the foreseeable future. I've got some things going on that require my full attention and I can't say how long I'll be dealing with them, so don't be alarmed if you contact me and don't hear back for awhile." and then let the "friendship" fizzle at a pretty quick rate.