Indefinitely barring stupidity and/or major injury. If I have a knife and access to water and fire, I’m good. I can make the rest (and have, although not “to save my life.”) Survival training and a lifetime of backpacking comes in handy.
Although it’s uninhabited, it is a tourist destination. I think I’d survive ok; I would be sure to visit the highest point on the island, Mt. Dick.
I decided to go with indefinitely, but it’s actually pretty hard to say…
With matches and water, I can certainly make it a few days. I don’t think I can make fire on my own once the matches run out, but I’m famous on camping trips for only needing matches once - I keep the coals buried right so that the next fire is built from last night’s coals. With 40 matches, that gives me decent coverage for the accidental time when the coals are lost.
I’m not much of an outdoorsman when it comes to building shelters and weaving baskets, etc. but I think I’d manage in an environment like that. The knife would be a huge help there.
Getting enough food is a concern. I see there are birds and presumably fish and shellfish. I’m not a hunter, don’t fish and know little about foraging. I’m just not sure whether I’d have enough food. I also don’t know much about the density of the bird populations or whether they’re seasonal. Overall, I think I could forage along the beach to meet my protein needs - I do at least know how to find and gather mussels, clams, crab, etc.
As far as health goes: without my glasses, I’m darn near blind, but I can actually fake it pretty well. I have asthma that requires an inhaler a few times a year… but I think I’d probably live even if I didn’t have an inhaler. (In fact, my current inhaler expired four years old; don’t tell my doctor.) Other than those things, I’m pretty healthy.
I voted a year or two.
In Boy Scouts I did a 3 day survival hike. Given that water is available, I could probably manage to get enough food to sustain myself. I could probably also manage heat and shelter OK.
Someone made the point that if you could survive a year than you could survive indefinitely, I would not be so confident about that.
The 3 main concerns being
Only having limited recall of edible plant knowledge I might screw up and poison myself -instant death or serious illness would probably both be fatal.
Injury- infection or mobility limitation could be fatal.
Illness - any virus or bacterial illness could either be outright fatal or limit the ability to gather food/water to the point of killing me. Long term things like scurvy or some other nutrient deficiency also become a real possibility. Especially due to the limited diet I would have (the few plant I know are safe + whatever protein I can manage to catch)
Me too. I’d say a few days without my meds.
Me too. I could last two weeks, but they would really suck.
If I am not rescued or dead after a year or so, I’m taking the knife to my own wrists.
A year or two; I’ve had some survival training and I am healthy and quite fit. Also was a commune/farm kid for years and retain some knowledge of hunting, fishing and other such skills even though I haven’t used them in decades.
However at 56 years old I’m at an age where Bad Things can happen easily, health-wise. And I’m less physically resilient than I was 20 or 30 years ago. So without medical care, if I’d get sick or injured or infected, I probably wouldn’t last long. Also I can’t see any fine detail worth a shit within about eight feet in front of my face, so without glasses I’d be quite compromised.
I answered a week or so, but I might be overestimating my abilities. Between scraping up a few non-threatening looking plants and building a lame, amateur fire, I’d hang on a while before dying of hypothermia/starvation/thirst/infected wound/suicide/whatever. I’d turn into a vegetarian, because I have no illusions about my hunting skills, and would stave off the boredom by spending my time writing.
ETA: Oh, and if I don’t have my glasses, you can consider me dead. I’ll probably fall into a 50-foot deep hole or something and get eaten alive.
Thanks to my military training I’d probably be able to get some fire and shelter going and could last a pretty long time, assuming I didn’t go insane from isolation.
Shelter is a big deal. Auckland Island is cool essentially all year, and wet. You can die of hypothermia and never knew what hit you in such conditions.
I’m another one for “indefinitely”. Two liters of water gives me plenty of time to find natural sources, and I have actually built an adequate shelter in a day and slept in it over a winter night. I haven’t had as much experience as dracoi at keeping embers going, but I’ll have plenty of incentive to learn, and 40 matches is enough for a lot of margin of error. Nor is finding edible plants as hard as most people think: Very few plants are actually poisonous, and most of the ones that are will make your lips numb or otherwise warn you before you get a lethal dose. “Edible” mostly just means that you can chew it up and swallow it without too much effort.
Not only that but seaweed and other sea plants areextremely nutrient-dense and nutritious. Just go down to the shoreline and pick your greens. 
And many sea creatures (octopus, shallow-swimming fish, shellfish) are easy picking as well. When I was a kid, catching octopus, shrimp and certain fish was literally as easy as shooting fish in a barrel. As an under-10-year-old us kids would often go forage for everyone’s dinner. Limpets and other crustaceans were a no-brainer - you simply pick them off rocks.
Without my antidepressant meds, it’d be fetal position and dead in a week. Unless, without my lithium, I went totally manic and then I’d probably think I could swim and dive off a cliff. Instant splat.
I should have picked the “Another period of time not specified” option.
I’d give myself ten minutes.
I’d say indefinitely.
While I’m not major league outdoors, with those items I reckon I could go for a while. There’s water there, if there isn’t some form of shelter built by others that I could use, then making something shouldn’t be that hard. Priority would be to get a fire going for warmth and keep it going once I got some decent shelter organised.
Water shouldn’t be an issue and there is access to food.
Knife, matches and a water container?
I’m golden.
I’ve hunted, fished and built my own shelter a few times.
Subantartic island*? I hate cold. I’d prefer not to have to keep a fire going 24/7 and eat moles, cause I’m not going to be very good at fishing or hunting birds with spears. I suppose I could eat penguins (see below)
*To be honest, up til this very second I never knew an uninhabited island that large existed on Earth. If I woke up on that beach to see mountains in the distance, and no one around…I might think I’d gone back in time.
My next instinct would be to circumnavigate the island looking for a village or something. After a couple of hours of that, I’d realize how dumb that was and I’d better find water and shelter.
So it really comes down to how quick I run across some water or some penguins to brain over the head
I suspect there are things that people aren’t taking into account sufficiently here. According to info upthread, it basically rains every day and is never much above freezing. Further, the island are in the “Furious Fifties” ie it is windy all the time. With windchill factor, and being wet, your heat loss is going to be severe.
Fires are going to be very hard work and risk dying of exposure is going to be absolutely extreme.
The OP says you are dressed in “sodden casuals”. This could mean anything. If this means full fleece or wool clothing and a waterproof layer, I would give myself some fighting chance of lasting the first night. If it means lightweight clothing and no waterproof layer, I think I would be pretty screwed and I think most people here are kidding themselves if they think they would be much different.
Indefinitely, I think.
Big one for me would be keeping warm in the cold season, although I know how to make cordage and weave mats, so I might end up wearing some absurd grass-stuffed basketwork suit of armour in the winter.
Rocky coasts are usually pretty productive for seafood - shellfish on and under the rocks, vertebrate fish trapped in tide pools.
I’m not very familiar with the edible plants of the Southern hemisphere, but might be able to guess at the edibility of some if I recognised them as relatives of cultivated garden plants and shrubs. If anything looks abundant and nutritious, but is unidentifiable, I might try to trap a mammal species and force feed it to test.
I could last indefinitely, I think. I was very much into camping and survival skills when I was young. When I was a teenager, I took part in a program called “outdoor challenge” where we basically had to survive on our own in the woods for a week. I also did a program in the winter where we basically did the same thing, except in snow (they gave us food to make sure we wouldn’t starve). When I read the OP and saw that it included a knife, I thought “well hell, this is going to be easy.”
Since I’ve basically sat behind a computer for the last 30 years (and now have the body to prove it), forcing me to run around and actually do things for my own survival would probably do wonders for my health. I sure would miss the internet though.