Is a minority government forced to hold an election if they lose support from the crossbench?

If a minority government lost their majority support in the House of Representatives, an election would not automatically be held. 

Firstly, the government could negotiate with other independent and/or minor party members to try to secure a new majority.

If the government was unable to secure a new majority, the Governor-General could approach the Leader of the Opposition to see if the opposition was able to secure the majority. If the opposition had gained the support of the majority of the House, the Governor-General would appoint the opposition as the government.

If neither the government or the opposition has the support of the majority of members of the House, the Governor-General may call for an election to be held.