Does leaving Australia and coming back give you a fresh three months?

Each arrival starts a new period of up to 3 months, so a trip to New Zealand or Bali and back does reset the per-visit clock while your visa is still valid.

But the visa is a visitor visa

The eVisitor is granted on the basis that you are visiting. Someone who spends nine of twelve months in Australia, leaving only briefly each time, is not visiting — they are living there on a visitor visa. Border officers look at the pattern across your passport, not just the current entry.

What you may be asked to show on re-entry

• An onward or return ticket
• Funds to support yourself for the stay
• Evidence that you are going home: work, study, a lease, family
• A reason for returning so soon

If entry is refused

A valid visa is permission to travel, not a guarantee of entry. If an officer is not satisfied that you are a genuine visitor, the visa can be cancelled at the border and you can be sent back on the next available flight. That record then follows you into future applications.

Source: Department of Home Affairs — eVisitor (subclass 651)