A Sydney homoeopath and his wife have lost an appeal against their manslaughter conviction for failing to obtain proper medical help for their baby.

Thomas Sam was jailed for at least six years and his wife Manju for at least four after their nine-month-old daughter died from a severe skin infection in 2002.

Their daughter Gloria was so sick with eczema that she constantly cried in pain, her skin broken and oozing fluid, a Sydney court heard last year.

They repeatedly rejected conventional medical treatment and instead opted for homoeopathic remedies.

When the child died, three days after being admitted to hospital, she was malnourished and her immune system weak.

A jury found them guilty of manslaughter by gross criminal negligence, by not seeking conventional medical help.

A sentencing judge described it one of the most serious cases of its kind.

The Court of Criminal Appeal has dismissed an appeal against their conviction and sentence.

Thomas Sam is banned for life from practising homoeopathy in Australia.