The new command he was given was arguably the most important command in Australia at the time. So obviously there was still enough people who liked him for him to be given such a command. You don't become a Brigadier General at 29 which is younger then me man if your a numpty.
Based on my readings of Blamey, and Australia in the Pacific in WW2......And the actions General White's career I honestly think he was hard done by. You don't go being the 3rd most senior ranked general in an army at the outbreak of a war, and after a single defeat in a situation outside of your control to ending the war all but forgotten.