The Minister has powers under the Migration Act 1958 to to intervene in your case when the Minister thinks it is in the public interest to do so.
What is and what is not in the public interest is for the Minister to decide. The Minister is not legally bound to intervene or to consider intervening.
When the Minister intervenes to make a more favourable decision, this usually means that the Minister grants a visa. However, only a small number of all requests for ministerial intervention are successful.
Options that might apply to you: