I don't believe that mining businesses like Rio Tinto Limited (ASX:RIO) and BHP Billiton Limited (ASX:BHP) are buy-and-hold type businesses.
The nature of commodity industries like mining generally means that, whenever prices rise to levels that are attractive, additional supply enters the market.
For example, when iron ore was $140 and miners were printing money, additional miners with less attractive resources and higher costs were able to enter the market and make a profit. The additional supply, coupled with only modest growth in iron ore demand (businesses don't use more steel just because more iron ore is getting mined) eventually caused a collapse in prices.
The same thing happened with the oil and gas industry, and I believe the same thing will eventually happen with the lithium and cobalt industries. Those industries may be a way away from reaching equilibrium, if forecasts for lithium demand are accurate, but the same risks of rising supply apply.
Additionally, the business model of miners is not all that attractive compared to, say, a supermarket. Miners spent enormous amounts of money up front drilling holes in the ground and then building a mine. Once the mine is built, most of the money goes to paying off debt that was required to build the mine, and then most of the money after that goes to drilling holes in the ground to find another mine to build or to expand the current one before it runs down.
That's fine when prices are booming, but it generally results in lower dividends, fewer share buybacks and means that the business remains capital intensive and vulnerable to commodity price swings.
As a result I don't think shareholders should aim to hold miners forever. A wiser strategy could be to buy when there's 'blood in the streets' and share prices are depressed, as the cyclical recovery can be very lucrative. You just need to make sure your miner is one of the more cost efficient in the industry (so it is still profitable at lower prices) and has survivable levels of debt, so that it doesn't go broke while you're waiting for the recovery.