It’s difficult to say who’s responsible solely on the basis of your description, but generally speaking the sewer line that connects the Lots to the communal sewerage system is Common Property, and the responsibility of the Owners Corporation (Strata). That conclusion is supported by the by the fact that the Strata Manager is arranging for the problem to be rectified whenever you make contact.
There could be a number of reasons for the Strata Manager’s lack of action in attending to the repairs of the sewer line, like perhaps they’re waiting for the Plan’s Executive Committee to make a decision, or maybe the Owners Corporation is short of funds.
None of that addresses your concerns though, so why not write to the Strata Manager advising that on the next occasion a surcharge occurs, you will make contact the local media. Personally I dislike that approach, but as you’ve tried everything else ….