I remember discussing this in a Constitutional tutorial. It was pretty heated. Can't really remember what was said and I won't bother with my notes (because I don't know where they are), but one of the reasons the 1999 referendum failed, in my opinion has to do with the advocates of a republic. They seemed to be out of touch with the average Australian. Further, there seemed to be too much emphasis on significantly altering the Constitution, and whilst a minimalist model was proceeded with, the damage had been done.
As it is, there is no need at the moment for a republic. Everything in the history of the Australian government, with the exception of a few interesting bits (rum rebellion, Jack Lang, Payroll tax cases etc), has been pretty smooth and gradual. We gradual gained out judicial independence in 1986 (that was officially. There is speculation among scholars that the Privy Council had no power from either the 30s or the 50s - interesting reading).
At the moment a lot of our population are elderly and many of them staunch republic supporters. Add to that, no great benefit has been convincingly demonstrated, there is no reason why the referendum shouldn't have failed.
In 20 or 30 years we may become a republic, or progress closer and I'm almost certain I will see it in my lifetime, that is barring an early death or a drastic alteration in the state of world politics.
And everyone who keeps using America as a great example of a republic - take a closer look. Australia, in generai, has less social inequity, less internal problems and a great deal less arrogance. America is sort of like the rich tycoon who sells his soul for money and power, but deep down lacks something.