I can't really answer that because almost all of my research on Water Fasting has dealt with it as a healing modality. For optimum healing, complete rest is needed so the body can channel its reserves into cleansing. I did read one article that said that ultra low calorie diets and fasts must be avoided when doing strenuous exercise because the additional need for fuel (glucose) can result in muscle wasting. Apparently the muscles do not utilize ketones like the brain and heart and rely on glucose even if they have to begin breaking down themselves. That is why I believe it is best to incorporate occasional water only days into an overall dieting program, whether its low calorie foods or juice fasting.
One way you can help maintain some of your metabolic rate when Water Fasting is to do deep breathing exercises. Still, you can expect the rate to drop significantly, this a part of the body's survival mechanism.