He's still alive! In fact, yesterday I saw the first normal lamb-berry poop in a week, although there's not much of it. That's not surprising given the fact that in the last four or five days, he's only been consuming supplements and a few ounces of goat milk -- like three or four ounces in 24 hours, which is nothing substantial. This morning, he drank three ounces of milk, which is the most he's ever had at one time, and he was sucking like he would have liked more. I decided to wait a couple hours, and I'll head back out and offer him another couple ounces.
Since this was a dam-raised lamb, giving him a bottle is not an easy task. It's like feeding a very clueless newborn. He spends a lot of time chewing on the nipple, and I'm constantly redirecting it to the center of his mouth, where he can suck on it. But other than a syringe or stomach tube, this is the only way to get anything into him, so for now, it'll do.
Even though he still can't lift his head, I'm getting very optimistic. It is completely amazing to me that he is still alive and fighting. Once a goat goes down, they're either dead or visibly better within 12 hours. I've never had one hang on for a few days, much less a whole week. This little guy is such a fighter!