I tried to find this answer on the web but could not find a firm number. I believe it must be in the 1000 calorie range, but for someone who is immoble, it is likely less. The best indicator would be if she is losing weight.
In general, a person can live a very long time without eating but hydration is another issue. With out taking fluids, a person will live only a week to 10 days.
A nurse at the local Alzheimers has seen people exist for a very long time on only nutritional suppliments, the only thing some people with dementia will consume in late stage. Suppliments can be thickened with baby cerial if needed (Much better than thicket, which doesn't taste very good)
Please read the following article. Make sure she is getting medical grade, high calorie suppliments.
FAQ29 - Dealing with Poor Appetite
http://www.prohealth.com/alzheimers/blog/boardDetail.cfm?id=58194#58262
[This Message was Edited on 09/16/2009]