Such a frustrating situation... I feel your pain!
I agree with @Rosey1
Enteritis is kind of a catch-all term meaning, essentially, a bellyache. "Weaning enteritis" indicates that it's happening at the typical age of weaning, which covers that 5-8 week age group. Weaning enteritis can hit fast, with no apparent symptoms (other than the kits are dying!). I've seen kits popping around at 8am, sitting looking miserable at noon, and flat dead by 4pm.
Sometimes it's a single kit, but other times you see the sequential deaths you're describing.
The shift from milk to solids seems to be a challenging period in the life of a rabbit, and some breeds and genetic strains seem to have a harder time with it than others. Keeping the diet the same as they and the mother have been eating all along is important, and giving supplemental probiotics like Benebac can be helpful too.
If I'm not seeing symptoms of coccidiosis, I tend to avoid giving meds like Corid, since that results in yet another disruption to the kits' gut situation. I do make some exceptions but I'm not a fan of prophylactic use of meds in most situations, as I'd rather raise animals that are healthy without the addition of meds. Also, eventually we probably are going to start seeing cocci that are resistant to amprolium.
But basically, any
change in the life of a rabbit can throw it for a loop, and often where that loop ends up is in their gut. It could be that given the stress of weaning, the constant fluctuations in the weather pushed the kits' stress meters over the top. It could also be that the pairing of the partiular dam and sire resulted in kits that were not optimally healthy and just naturally more inclined to succumb to weaning enteritis.
I would also consider what @judymac
said about the possibility of bad/moldy hay, especially if you've been having wet weather. Ironically, the first inclination most of us have to help sick rabbits is to give more hay; but speaking from sad experience, it does not take much moldy hay to wreak havoc in a rabbitry, and you end up hurting the very rabbits you're trying to help. The smaller and less vigorous rabbits are more likely to suffer from smaller amounts of exposure. If it was me, I'd give my hay a very close look and sniff (which would be a real sacrifice for me since I'm extremely
allergic to mold myself!).