rental AC has been down for a month

I moved into a new rental in Sydney exactly a month ago now and the only AC we had in the living area broke down/stopped working within a week.

I contacted the REA the day after, and she told me she contacted the owner. Now a few days later I couldn't contact her anymore because the holidays started and until early Jan I couldn't call them. Now in between this, We got an email saying the REA org had changed and since Christmas break still wasn't over, I couldn't let the new people know/follow up either

Finally, I was able to talk to/email the new REA and they have emailed me back saying they have contacted the owner and expect a response shortly.

That was 6 days ago and no response.

I would like to know if this is normal and if it's rude to ask for another follow-up. Also, since the AC has been down for so long, am I eligible for any kind of rent reduction? I still have 12 months left on the lease

EDIT update: they decided to replace AC outright and thats taking a while too now. https://www.reddit.com/r/shitrentals/comments/1iavakr/ac_replacement_in_place_of_a_repair_taking_well/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button