Logan inherited two-thirds of his mother's $1.8 million estate and all of his stepfather's $2.2 million estate and argued against his brother's attempts for a share Mr Luxford's estate.
The decision was handed down by Chief Justice Dame Sian Elias, Justice Sir John McGrath, and Justice Sir William Young.
Justice Susan Glazebrook argued against the decision, and said she would have allowed Alyxe's appeal to go ahead if she was not outvoted.
In the decision, Chief Justice Elias said the result centred on whether or not Alyxe was considered "living" at the time of his mother's marriage to qualify as a stepchild eligible to contest the will under New Zealand law.
"The result is hard for a number of reasons,'' her decision stated. "The claimant ... has special needs because of intellectual disability and may be thought to have a strong claim to provision out of the estate.
"There is evidence that the stepfather gave instructions for a new will, in which the claimant would have benefited equally with his brother, but it was not drawn up by his solicitors before the stepfather's death.''
The Family Protection Act did not recognise unborn children as stepchildren, the decision said.
"Although the appeal had highlighted `some anomalies and inconsistencies' in the Act which the Court thought `may warrant the attention of Parliament', it concluded that it was necessary to dismiss the appeal.''
Alyxe is cared for by his guardian, his aunt Susan Wood.
It was understood that Alyxe could still contest a share of his mother's estate, and decision noted he had a ``strong claim``in doing so.
