An interesting discussion. Because we breed breeding stock of a hardy native breed, we do need our ewes to be excellent mothers, and they will hand this quality down through their ewe lambs. However, I wouldn't necessarily cull after a single problem, but would give the ewe another chance. We have reduced our flock size in recent years so would be more likely to keep a ewe on for a second try now, compared to when we had a larger flock to manage.
If you think about it, a ewe which rejects one of her lambs may well in fact be being very practical. If climatic conditions, food supply or even some minor health problem will prevent her from rearing twins, then by rejecting one she is giving the other a chance at survival, rather than losing both. In the wild, mothers (such as elephants even) will abandon their baby to save their own lives - no point in losing an adult when the young are more expendable. This will be a natural instinctive behaviour. It is something which I have heard that Soays on Hirta will do (I haven't been there so only second hand info) in a bad year. In many parts of Britain this winter has been awful, so perhaps this ewe feels she can rear only one lamb.
There is also some evidence that animals can sense illness in others, and this can be a cause of an abandoned lamb, especially when it's one of twins which is rejected. If the dam detects that a lamb has something wrong with it, she will refuse to give it any more of her valuable time. We experienced this with a couple of Jacob ewes, which both rejected one of triplets. They both had plenty of milk so it wasn't that. In one case the lamb died within a few days of birth. The other was bottle reared to 4 months when it dropped dead with a heart problem.
Mothering ability is known to vary between breeds, with Suffolks scoring near the bottom and Hebs near the top and I do think it's important in breeds right across the board, to breed for good mothering, as well as for good conformation, longevity, good feet, good teeth and so on.
However, Abbaye has only a handful of ewes so will be able to give more care to that small number, and may well be prepared to give her ewe another chance.