Regrettably, apart from the approach to your Owners Corporation (O/C) there's not much else that you can do! However your O/C is in a position to approach your neighbour about inspecting the balcony drainage (see next para) and about limiting “spillage” outside his/her Lot; particularly as that is affecting other residents and perhaps the Common Property (below).
Depending upon the age of your Building and the design of its balconies, there may be a drain through the bottom course of any bricks or render at the balcony edge, or better still a floor drain that's connected to the stormwater.
Constant hosing-down and watering (of pot plants) can cause dirt and debris to block these drains, or again depending upon the age of the building, any drain hole/s just through the brickwork can have a spout extension added, so that excess water emerges say 300mm away from the outer edge of the balcony, thereby missing yours.