The number of uranium mines is declining, and eventually, perhaps as soon as 2050, there won’t be any more. It is not that there will eventually be no more uranium. It is one of the more common minerals in the universe and on Earth. But on Earth, the vast majority of uranium is too scattered to be of any use. Uranium is needed for nuclear power plants, where it is used to generate electricity. Uranium is useless for that purpose if the energy needed to extract it is nearly as great as the energy generated from it, and that would be the case with the vast majority of the uranium on Earth. It is either too deep underground or underwater to get to in the first place, or it is in concentrations so low that the energy cost of digging would be greater than the energy value of the uranium.
But we will not be out of uranium when the uranium mines are exhausted. Already, a significant fraction of new uranium is mined as a by-product. It comes from a mine that is being operated to extract another mineral, such as gold or nickel. Any mine at all can dig up traces of uranium. At a small fraction of mines, the uranium is concentrated enough to be worth separating it from the other materials. This will become practical at more mining operations as uranium becomes more scarce and is price goes up.
It is a plausible job for robots, which might be designed to detect and separate uranium along with other mineral by-products without being harmed by the radiation. Advances in robotics could make small-scale uranium extraction a routine part of mining.
All of this will not be enough to power all the nuclear plants currently under construction through their potential useful lives. Even before all of these plants go online, some will surely have to be converted to operate on another energy source because of the high price of uranium. But at least a few nuclear power plants will be able to continue to operate beyond the end of the century.