My perspective is that the EC has a strict statutory duty to maintain the common property and should undertake these repairs as quickly as possible to avoid further damage and a possible greater expense.
Undertaking the repair is the most important thing. Any dispute between the EC and a Lot owner about culpability or contributory negligence should happen after the repair and not before the repair. Both the repair issue and the culpability issue are two separate issues. Based on your comments, in your elderly mother’s neighbour’s situation the EC would be unlikely to succeed in any such claim.
If I was in the position of your mother’s neighbour then I would be writing to the EC and reminding them of their duty to repair and maintain the common property in accordance with both the Act and the Tribunal Ruling, and reminding them that any attempt to claw back the costs from any Lot owner should occur after the repairs have been made.
The EC, on its own, cannot appeal the Tribunal decision. Any appeal must come from a decision of the OC at a general meeting. If the other owners are “sick of the matter” then they should not support the Appeal and should vote against any Motion that the EC proposes regarding continuing with an Appeal on this issue.
In response to your question about damages, a recent Supreme Court case (The Owners – Strata Plan No. 50276 v Thoo) appears to have removed the lot owner’s private right to damages for breaches of an owners corporation’s statutory duty.