Do you really have the ability to ask for a refund for a full two years?
You can ask for a refund for as long as seems reasonable. However, ultimately it comes down to what the adjudicator in your state or territory's fair trading tribunal thinks is reasonable - or, maybe, what you can convince the retailer they would find reasonable.
The amount of time that's reasonable would probably depend on the nature and price of the item. If it was something that should reasonably be expected to last, say, 5 years, you could possibly make a case for it to be replaced or refunded for up to that length of time. However, it's likely the tribunal would be less sympathetic to that as time goes on - although it may depend on how much you would be inconvenienced by repair.
With cheaper goods, it may come down to how much it will cost the retailer to defend themselves in the tribunal versus the cost of replacement or refund - particularly if you convince them you know your rights and will put up a good fight.