The drop in incentive to secure the network with increase in mining to the point where most of the 21M supply of BTC is a real challenge.
Right now, miners mine because they are incentivised to do so by receiving rewards with every mined block but as that community becomes smaller and smaller, people would probably take a different angle to security because then there's no point in holding a very scarce assets like BTC if it's not valuable due to next to no security. Which groups will take that approach if security doesn't become obsolete in the next 100+ years is something I can't even start guessing as most people today will not be around then, and technology can take us much further in a century.
It is a far future and we can not know what will happen in the world and with bitcoin network & price in next 120 years.
Bitcoin miners receive income from block rewards and confirmation rewards (as transaction fees). If in next 120 years, the price of Bitcoin is a few millions of dollar and miners receive very big income from transaction fees by confirm transactions, I think they will keep mining.
They care about income, to pay power bills and to get beneficiaries. From where the income comes from, block rewards or transaction fees, it is not a big matter for bitcoin miners.