One thing I forgot to mention above was that there should've been another draw - Adelaide 2006/07.
But anway - on raw results, between 1989 and 2006/07 Australia lost 35 games. 12 of these can be broadly classified as "dead" (including 2 against England where the series was still alive but the destination of The Ashes was decided).
The others are:
Trent Bridge and Edgbaston (should've been Old Trafford too) 2005
Adelaide 2003/04 vs India
Chennai and Eden Gardens 2000/01
Kandy (should've been Galle too) 1999/2000
Kensington Oval and Sabina Park 1999
Eden Gardens and Chennai 1997/98
Kensington Oval and Bourda 1991
These 12 can broadly be classified as coming in series in which they were fairly well (sometimes comprehensively) outplayed - though those against India in 2003/04 and in West Indies in 1999 were drawn. There were also one-off Tests at Delhi in 1996/97 and Basin Reserve in 1989/90 which were lost.
The remaining 9 are:
Edgbaston 1997 (went 1-0 down and ended-up winning)
MCG 1996/97 vs West Indies (2-0 up going into this match)
Queen's Park Oval 1995 (this loss made it 1-1 but they won the next game to win the series)
National Stadium Karachi 1994/95 (a defeat by 1 wicket, thanks to the batting of Mushtaq Ahmed
This goes down as one of the great "how did they lose?" games of all-time)
The Wanderers and the SCG vs South Africa 1993/94 (2-2 draw in this 6-Test home-and-away series, both defeats putting Australia 1-0 down in the respective "leg" from which they came back)
Eden Park 1992/93 (a loss which enabled New Zealand to tie a 3-Test series)
The WACA vs West Indies 1992/93 (comprehensive defeat in a deciding Test)
...aaaaaaaaaaaannnnnndddddddddddd Adelaide 1992/93 (which needs no explanation - 1 run, though apparently it shouldn't have gone anywhere near that close, to set-up the above decider)
That's 5 live home Tests they lost in 18 home seasons.
And 2 of those were by wafer-thin margins (Adelaide 1992/93 and SCG 1993/94).
Just 3 times at home, and 17 times away, were Australia been easily beaten in the 1989-2006/07 period. And in this time they played, let's remind ourselves again, 195 Tests
(excluding World XIs, Bangladesh and the Zimbabwe of 2003/04, against whom they won every game). Of course, there's the odd victory (already mentioned Adelaide 2006/07, there's also a game in Sri Lanka in 1992 that Sri Lanka should have cantered to victory in) that really shouldn't have been one. But that's 2 occasions - even had they gone the way they should have, Australia's record would remain astonishing.