Hi RMV. I am sorry your wife is feeling so bad. Babesiosis can cause lack of appetite.
Are you aware of the Jarisch-Herxheimer Reaction (herx)? Often when people who have Lyme take antibiotics, their symptoms get worse or they get new ones. When the antibiotics kill the bacteria, toxins are released making them feel sicker. It can be scary when it happens, but it is a sign the antibibiotics are working. Although it can vary individually, many people experience this at the beginning or change of treatment and every three to four weeks. With Babesiosis, some people experience this on day three and every three weeks.
Here is one site where you can read about the herx: http://www.angelfire.com/biz/romarkaraoke/Herx.html
I have had a severe case of Babesiosis, so I know how intense the herxes can be. Make sure you are documenting your wife's symptoms daily. One way to do this is to list the main symptoms she has each day with a numerical rating of their severity from 1-10. Over time when you review this, you can see when her herxes occur and how she is responding to the meds.
It is good her infection is relatively early. Over time as the infection load decreases, the herxes should get less severe. It can take time to recover and it is normal to feel worse before feeling better. With proper treatment, she can get better. Make sure she is doing everything possible to strengthen her immune system such as eating healthy, taking appropriate supplements, drinking a lot of water, doing things to detox, getting enough rest etc.
It is also important to learn as much as possible. I recommend reading Dr. Joseph Burrascano's 2005 Diagnostic Hints and Treatment Guidelines For Lyme and Other Tick Borne Illnesses at http://www.ilads.org/burrascano_0905.html He is one of the top Lyme doctors in the country, and many Lyme doctors follow his protocols. He also lists diet, supplement, and exercise recommendations. I also recommend the books "Everything You Need To Know about Lyme Disease Second Edition" by Karen Vanderhoof-Forschner and "The Lyme Disease Solution" by Kenneth B. Singleton MD.
Your wife is lucky to have your support. Hang in there okay?