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Thanks for all your suggestions. I did take him to the vet as advised, who diagnosed a virus and gave him an injection of antibiotics. The next moring the kitten had a violent convulsion, so we rushed him straight back to the vet who wasn't concerned by the convulsion and administered another injection. Sadly the convulsions continued and grew more frequent, and the little chap passed away in his sleep. We were distraught, and especially being around Christmas time didn't help matters.
I'm now keeping a close eye on my other kitten, who hasn't shown any signs of the virus (if that's what it was - I have my doubts).
I'm not sure what I could have done differently to avoid losing my kitten - perhaps he was just to weak to fight it and there was nothing I could have done.