The West New Guinea Dispute of 1958-60;
Konfrontasi 1965;
East Timor 1999.
In the first two, the US Government outright refused to intervene or guarantee Australian security. In the third, the US Government failed to provide much in the way of material means during the crisis, despite being requested to do so. In all three, the Australian Government approached the US Government and while we did not attempt to invoke the A**US Treaty, it did form the basis of the approach.
I do not include the 1975 Indonesian Invasion of East Timor, as the Australian Government aquiesed to that after learning of the backing the Indonesians had already received from Washington.
Australia and Australians IMO all too often fool themselves that the A**US Treaty is some magic blanket which provides a foolproof means of ensuring US protection. It does not. It is a very poorly worded (from our viewpoint) non-Guarantee of security consultion and nothing more.