EatQOD

I suggest looking at this nice review paper: This whole area is a bit controversial. There is no controversy that the metabolic rate falls initially, but then it may go back up when measured several months later. Also, the prime determinant of metabolic rate is muscle mass, so if you lose muscle mass, your metabolic rate will go down no matter what. In the Heilbronn paper cited in this section of the forum, she and Ravussin measured metabolic rate 21 days after QOD ad lib eating, and metabolic rate did not change.

Anyway, here is some evidence about the time course of how metabolic rate drops when fasting. Read the whole paper - it's fascinating! But especially the excerpt on page 4 (reproduced below).

Feeding, fasting and starvation: Factors affecting fuel utilization
Authors: MacDonald, I. A.; Webber, J.
Source: Proceedings of the Nutrition Society, Volume 54, Number 1, March 1995, pp. 267-274(8)
The full text .pdf article is available.

page 4:
"It is generally believed that resting and total energy expenditure fall in starvation and underfeeding. Whilst this is undoubtedly true after a few days of undernutrition, it may not be the case initially. The classical studies of Benedict et al. (1919) revealed a modest rise in resting energy expenditure in the first 12 d of a prolonged period of underfeeding. This was followed by the expected fall over the next 30 d. Similarly, the first 2 d of total starvation are accompanied by increased resting energy expenditure (Mansell et al. 1990; Webber & Macdonald, 1994), which is likely to be due in part to the energy costs of gluconeogenesis, ketogenesis and fatty acid-triacylglyceroi recycling. The rates of gluconeogenesis and fatty acid-triacylglycerol recycling seen after 2-3 d of starvation could easily account for 5% of resting energy expenditure. As starvation proceeds there is a fall in resting energy expenditure, such that it is normally below initial values after 4 d of starvation (for review, see Elia, 1992)."

JT