I will say that both my basenji boys will skip a meal when it is really hot. My 2 basenji girls would never dream of missing a meal though and one of them could stand to once in a while :rolleyes:.
The thing that makes me wonder if it isn't food related or something medical is the throwing up. When he eats and throws up, is he gobbling his food down (eating faster because he skipped a meal) and so the food comes right back up undigested?
Also, have you purchased a new bag of food lately and has the meal skipping and throwing up increased since - because maybe there is something wrong with that bag. I've had that happen before.
Oh, and I don't give ice cubes because I'm afraid of breaking teeth. I do give frozen kongs though - peanut butter, chicken & rice, that sort of thing; and frozen marrow bones. And lots of cold water available.