One minute is the answer in Australia. Most initial descent clearances are given as 'when ready' so the one minute doesn't apply in that case.
Off topic but ATC will always facilitate an alternate clearance where possible. If they cannot due traffic or airspace then of course you have to do what you need to to keep your aircraft safe and ATC will continue to provide a SIS but you won't be getting a control service. I've seen aircraft fly through active restricted airspace (no longer receiving a control service and with ATC declaring an emergency) to avoid thunderstorms. Paperwork was submitted (as required) but there was no problem for the pilot or ATC. Everyone did their job and the outcome was a safe as possible. It is team work in the end.