It sounds like her mother is doing a huge disservice by keeping her home. If she is not acutely ill, there is no reason for her to stay home. Everyone is tired some days, and many of us cough EVERY SINGLE DAY but that isn't an excuse to stay home.
Her inactivity, in the long run, might even lead to her becoming even more sick. Exercise, working and playing at school, and getting out in general are keystones to keeping healthy.
Please do what you can to talk to her mother about getting her to go to school as much as possible. It will help her happiness overall too, to feel like she "can" do things, rather than feeling weak and useless. Also her getting behind is horrible - I was diagnosed in 3rd grade and spent about three MONTHS in the hospital and they literally sent me every single assignment, quiz, test and project, and I did them all from my hospital bed. You can't just gloss over all that work and expect to pass.
Good luck to her - please talk to her mother, or direct her here if you can.