Found an article showing how metabolic rate increases during the first 48 hours during a fast. According to this it would be optimal to fast 48 hours since basal metabolic rate is higher compared to overnight fasted value.
"During the first 2 days of starvation there is often a small absolute increase in BMR relative to values obtained after an overnight fast."
on the other hand
"Although the rate of protein oxidation (reflected in the rate of urine N excretion) is frequently considered to decrease during prolonged starvation, especially in the obese (see below), several studies have shown that there is often a transient early increase. "
Especially day two and three have increased rate of protein oxidation, making a 48 hours fast less favorable considering potential muscle loss.
Personally I think these are only short term studies and muscle loss is no problem when you fast on a regular intermittent basis.