Is there a plausible reason that the world might not be able to get any sort of metal from Earth, short of what we already have? I was thinking it could begin in our sort of "modern" day and age, but could happen over a relatively long span of years. I'm mostly looking for something scientific, but other possibilities could be considered.
Bioengineered bacteria or nanobots.
A hardy metal eating bacteria, most likely different strains for different metals, could significantly damage our stockpiles and in-use metals. Similarly nanobots using metal to create grey goo would destroy available metals. Both would also possibly destroy the mining equipment used to collect raw metals, further reducing our ability to replace lost metals.
We can run out of ore. It did happen once already; up until the early 20th century iron was produced from high quality ore with about 70% iron content but due to depletion and increased demand, iron is now produced from ores with 25% iron content.
If the world goes through another Industrial Revolution and demand increases significantly, it's plausible that we'll run out of ore (or at least cheap readily available ore).
At that point most of the steel would be used up in mega structures (spaceships, skyscrapers or whatever) and a shortage would occur.
I don't think it's possible to go completely without any metal - Earth has significant deposits of iron and you can always recycle, but if metals are prohibitively expensive, industry might switch to using other materials such as plastics and carbon fiber.
In a word, no. If we run short of any metal it becomes worth-while to mine less concentrated ores. Too many people rush in, under-supply turns to over-supply, the price crashes, and 3/4 of the new mines go bust. Rinse and repeat, probably since mining first started.
I used to think that the non-metal that we are in greatest danger of running out of, is oil. It's a special case because it's a liquid, and there are rare geological pockets in which it is concentrated and tap-able. We've found and tapped almost all of the big ones. Sooner or later, the Saudis will run out of oil.
But I was wrong. We've recently found how to extract dilute oil from large abouts of rock (Fracking). Extracting dilute metals fron large amounts of rock is what we've been doing to obtain metals for at least the last century, if not forever. FOr any metal, there are plenty of ore-bodies not yet exploited because the price has never been high enough for long enough.
As for energy: if we burn all the oil and coal we know of, we are doomed. But we've solved that problem also, and solar PV cells are not very gradually replacing fossil fuels. Methinks by 2100, fossil fuel burning will have ceased, and global warming will be left as a big but ultimately manageable problem.
Oh - and there is one other non-metal for which no alternative exists. It's (fresh) water. If you live more than 200 miles from an ocean and if your water is being produced by tapping an aquifer deep below your feet, beware. We can use solar PV electricity to make fresh water from sea water, but making it and transporting it in sufficient quantities to maintain arable farming in a remote desert seems implausible. Hence, there will be a water-driven global food crisis to come.
There's one, and really only one reason we would run short of any metal that was otherwise economically important and that would be that our net energy budget couldn't support the processing of that metal. The world consumes a certain amount of energy every day, of what isn't wasted one way or another a chunk goes to primary (extraction) industries like mining and forestry and farming, a chunk is involved with secondary (processing) industries that make goods from raw primary materials, and a chunk goes to tertiary (service) industries that provide less concrete things to people. If the population and energy availability every got screwed so that almost all the available energy needed to go into just feeding people then metal extraction becomes a secondary concern and the more energy intensive processes will have to go.