This is more some suggestions to investigate rather than quoted facts. Lactating animals given the opportunity eat more especially in early lactation so their BW could increase but actual "carcass weight" i.e. less feed ingested and digestive tract stay the same or decline. Late lactation under well fed conditions this can reverse. Given the variability of BCS and liveweight measurement relationship during this lactation period I would suggest an independent measure/estimate of carcass fat content such as ultrasound fat depth. 

Typically, the ewe's milk production peaks 3 to 4 weeks after lambing and steadily declines to about half as much by 10 weeks. About 74 percent of all milk is produced in the first 8 weeks of lactation. So, from 3rd month onwards its body weight should increase and that is happening. But, you have to look into the independent component of BCS which is reversing the trend. There is difference between body weight change (biological in nature) and BCS change (biological+mathematical). Hope thinking in this way will lead you to some conclusion. Also, this leaves scope for inclusion or deletion of some factors in BCS computation for age group-wise expressions. You should think in the line of partitioning of nutrient at specific stage also.

This is indeed an unexpected result. Do all ewes in your experiment follow this trend or are there subgroups that behave differently (pointing at an effect of parity or age that interacts with change in body weight?).

I assume you have ruled out any problem with the datacollection (e.g. issues with weighing scales or differences in scoring..). If this is the case, an objective measure of fatness (as proposed by John Colin McEwan) may shed some light.

More data is needed to fully understand what is happening in this case. One would expect both BW and BCS to decrease during the initial phase of lactation, a physiological phenomenon also seen in cows when animals are in negative energy balance and have to meet deficits by mobilizing stored fat reserves, thus, the loss in BW and BCS. However, this is probably a good observation that deserves further investigation to include the quality of feed offered to these ewes.   

Assuming that your data are correct, there is only one explanation for these findings: dense tissues have been replaced by tissues with less density. There are 2 tissues I can think of, which could result in these findings:

1. Muscle mass has been mobilized in the first weeks of the lactation (besides fat tissue), in order to compensate a negative energy balance. During the later lactation, the ewes have built up more fat tissue than muscle mass. Muscles being more dense than fat, this could partially explain a loss in body mass combined with an increased BCS. This could be due to an imbalanced feed ratio.

2. One should not forget and underestimate the skeletal demineralization process during the lactation, i.e. calcium mobilization from the bones, which may substantially reduce the body weight without impacting BCS. This effect is physiological to some extent, and can be modulated by the feed and mineral composition, from the dry period throughout the whole lactation.

I agree with what is being said also. The ewes could be depositing body fat, but not internal fat (along with muscle, but most likely fat). Also, BCS is not the most accurate measure and can be highly variable. I concur that in this situation especially, ultrasounding for back fat could answer a lot of your questions here and even taking body wall thickness measure sat the same time. Loin eye area might give you more information also.

Were the ewes always weighed using a standard protocol involving time of feeding, time of suckling and access to water? Was wool growth a factor? Was a single weight  taken or multiple weights over 3 days averaged? I agree with the muscle to fat ratio changes mentioned earlier. Was there a deficit of protein intake later in lactation that would have caused mobilization of muscle?

In the Undernourished group (receiving a third of total ration: 200g /day) the evolution of BW and BCS are comparable during the five suckling months. About the age, most of the ewes in the 1st group were 48 months, but in the second (undernourished) the ewes were aged between 24 and 48months.

The purpose of this work is to know the skills of the local sheep breed in two different production systems (extensive Vs semi-intensive) in local farming conditions. So, it’s difficult to align the framework of animal management, particularly housing; the frequency to water acces; the exact composition of feed ration...

What was the actual change in BCS in the group (and how many animals per group)?  What was BWT? Was the same device used to weigh animals each time (and its accuracy)?  Did the same person/team do the weighing and BCS each time and was their any known comparison made between days (using a standard measure)?  If there was only a small decrease in BWT and small increase in BCS then this is not improbable, however dramatic increases/decreases would be more difficult to interpret.

While it is possible to have various changes as discussed above, seems equally if not more probable that there is an issue with interday measurement.