Yes, it is possible to reactivate an ABN that has previously been cancelled.
To do so, you must submit a fresh ABN application. It is important to include the cancelled ABN in the form where asked to provide it. Instead of issuing a new ABN, the ATO will then reinstate your old ABN so that it recovers its 'active' status. This will be reflected on the ABN Lookup.
If applying to reactivate a cancelled ABN there is a higher likelihood that your application will be flagged for manual review by the ATO. This usually occurs where the ATO determines that further checks are necessary to determine your eligibility to have an ABN. Should you believe this to be the cause of your application going to manual review then it is possible for the applicant to call the ATO to discuss the application and hopefully have final processing expedited.
N.B. If you have previously held an ABN and wish to apply for a new one for the same entity, you will not be issued a different ABN. Instead the ATO will simply reactivate the old one.
This information is of a general nature only and does not constitute professional advice. You must seek professional advice in relation to your particular circumstances before acting.