This was inspired by something I came across when I was looking up something for the domesticated Australian megafauna thread.
What actually happened: There is some indication that a subset of the extinct Australian megafauna survived on Tasmania for about 4000 years after they died out in Australia, probably because at that time Tasmania was an island, so humans didn't get there for about 4000 years after they colonized Australia.
As the last ice age intensified and locked up more water in glaciers, around 43,000 years ago Tasmania became a peninsula of Australia, which it has been off and on through most of its existence. Humans flooded in and the surviving megafauna died out, though Tasmanian Wolves and devils survived there (as they did in Australia until a few thousand years ago). Tasmania became an island again around 10,000 years ago with the start of the current interglacial.
What might have happened: Let's tweak the land level a bit and have Tasmania remain an island throughout the last 50,000 years. We can put the water gap that stays even during ice ages anywhere between the coast of Australia and Tasmania. For the purposes of this scenario it would be good to have it close to Australia, because the larger Tasmania is during the ice ages the more of the megafauna are likely to survive. Small islands and big animal don't mix well long-term.
So, humans colonize Australia, but can't get to Tasmania without crossing an arm of the ocean. They had to cross a water gap to get to Australia in the first place, but tropical oceans are considerably more hospitable to primitive boat tech than cold temperate ones. Apparently humans didn't cross the historic water gap, so there is a reasonable chance they wouldn't cross this one.
So, some of the big Australian animals survive in Tasmania. Diprotodon itself didn't reach Tasmania, but a couple of horse/Tapir-sized Diprotodon relatives did, along with short-faced kangaroos, marsupial lions, and few other oddities.
So, how long would they survive? There are no signs I'm aware of that the Polynesians ever got to Tasmania, though they might have visited but not stayed due to the incumbent Tasmanians. I don't know if Portugal ever reached Tasmania, though my understanding is that they found parts of Australia. The Dutch definitely discovered Tasmania, so they might be the first to disrupt this marsupial utopia.
Standard disclaimer: Yes, I know that creating a sea channel off of Australia would create butterflies that would probably prevent there being a Portugal or Holland in their historical forms, but messing around with geography is way too much fun to avoid because of butterflies.