I think this sounds serious enough to ask your local council to have a look (since your committee seems reluctant to do anything).
Alternatively, you could seek emergency orders from NCAT for a proper building inspection as a matter of urgency.
The legalities are that the balcony is almost certainly common property and the owners corporation has a duty to maintain and repair it. They certainly should be fixing the membrane and possibly charging the lot owner for damaging it.
They also have the right to demand entry if they need to inspect common property to see if there is a problem.
Now, all of this could be handled by our friends at Strata Answers who will (for a fee) guide you through the process or even take on the issue for you.
They would be my next call. Click on the above link for their contact details.