Problems

I have more than a passing familiarity with this model of weed eater, and I've got a few ideas on the fuel difficulty. First, I think Linn is correct on the nervousness thing. Goats are plain spooky about environment. If they don't have a degree of comfort, they won't do anything to slow themselves down, like eat. A change in circumstance can cause a milker to go dry almost overnight, and I've seen goats go fairly long periods with very little food, just to get a familiarity with their surroundings.

Second, it could be the heat. Heat tends to cause a lethargy for goats. Their normally high activity level goes to nothing, and they'll avoid food in the daytime. Like all herd animals, goats aren't nocternal, but they'll eat alot more in the late evening/early night when its hot.

Third, I can only go by the picture (call me Dr. Frist) but these animals look very healthy. I wouldn't start to worry until the ribs become pronounced while they're laying down. When goats drop weight, it happens in a hurry, so if their really off their feed due to a medical condition you should know it right quick.

Finally, despite popular legend, goats can be damned finicky eaters. That veries from season to season, and even from animal to animal. I'm not sure what your sister is feeding, but she can test their appetites with apple slices or carrots.

I don't know if any of that helps, but ...