You need to renew your business name every 1 or 3 years, depending on your initial registration or previous renewal term.
You can only apply for business name renewal 30 days prior to the expiry date, or when ASIC nootice has been issued.
If you miss the expiry date, you can still renew your business name as long as it is still 'registered'. If you don't pay for renewal, ASIC will warn you that they will cancel your business name after another 2 months.
If your business name is cancelled, you will have to wait 6 months before you can register it again. During this time, no one else can register your business name. You can also ask ASIC to restore your business name within this period.