How do I get my mother, who has aphasia, to do more for herself?

It sounds like she is depressed. Anti-depressants don't all work the same for everyone. Some people get worse on one and better on another. Some must try several. It's horribly frustrating, as they take weeks to work, and it's hard for a caregiver to tell what is going on. That said, you need some help with this. If she sleeps all the time, maybe it's her meds or depression, but whatever it is, you are too stressed. RSVP has a senior companion program in many areas, where a senior is paid to stop in and visit awhile so the caregiver can get away. This is a Federal program, so it's worth checking your phone book for RSVP (may be called Senior Corps or Retired Senior Volunteer Program). I hope you can find ways to get out and do things for yourself so you can relax. Stress takes a toll on the caregiver and care receiver.
Take care of yourself,
Carol

The Council on Aging and Jewish Community Center are other good sources for information. Is your mother in language therapy? As I understand it, some patients with this condition have trouble understanding words as well as speaking the right words. It sounds as if she has given up, and you didn't mention language therapy, so not sure if it was ruled out as a possibility to try and improve her condition. Apparently there are computer generated programs to supplement a language therapist program, but she may not be computer savvy. For sure, there are programs out there to give you some relief, visiting nurses, etc. If you have some space for yourself, you'll be better able to deal with her problems as well. Good luck.

I agree with Carol above, regardless of your mom's eating or not, you should address your stress. Unfortunately, it is much harder for caregivers. Caregiver who cannot leave their loved one often cannot do what others do (vacation, weekends, heck you probably can't even get away for a couple of hours to go to the movies?).
Have you heard of Guided Imagery? its a proven stress buster.
On the eating issues; try things she likes, even ice cream, and dessert. Good nutrition becomes secondary to getting something, anything inside their belly.

The thing none of us ever addresses is CHOICE. You do have choices about your mother. If you don't know them, the state Council on Aging can help. We all have choices and need to remember that. You can look into putting her into a care facility and if she has no money, getting her into a state-run program. Sometimes when we think we are trapped without options we feel helpless and frustrated, but the choice is there, even if ours isn't one we like. Remembering that might help you decide what you can and cannot do and act accordingly.