This depends very much on the management firm concerned. Some may say no on the simple basis that every other key that goes out diminishes the security of the whole building.
Some may charge you a hefty returnable deposit, some may charge you a fee. The thing is, there is no strata or rental law regarding this. If you have a key to the building and your flat, all obligations have been met.
Some might suspect you are sub-letting on airbnb and send you packing.
But if you are genuinely worried about losing your key, simple solution – get a keychain that attaches to your belt, like this one
or this one
… and relax.