The All Blacks extended their hold on the Bledisloe Cup to 16 years last weekend as they enjoyed another comfortable win over the Aussies.
Cheika's men have lost 38-13 and 40-12 to the All Blacks in recent weeks and some sections of the Australian media have called for him to leave.
However, Rugby Australia chief executive Raelene Castle insists the governing body are behind him, although she admits that recent results are a worry.
"He's contracted through to the World Cup," said Castle.
"He's got a plan, we're across that plan, we're comfortable with it. But clearly, you can't just ignore the performances, they're not acceptable.
"So, it's about what can we do to support him as an organisation, to make sure he's got what he needs to make sure the Wallabies are successful as we lead into that World Cup.
"Certainly, from our perspective, the board and myself, our support's behind Michael Cheika."