What is the incentive for continuing to mine bitcoin as we get very close to the 21 million cap? The Investopedia article on Bitcoin explains the Bitcoin issuance schedule and how it's halved every four years. Currently, roughly 18.5 million have been mined, with the total cap being 21 million. It's assumed that the last Bitcoin will be mined in the year 2140, which is obviously quite a ways off.
Given both the monetary and energy cost of mining Bitcoin (the two are related since it requires a large amount of computing power), isn't there a diminishing incentive to continue mining Bitcoin as we approach the hard-cap limit of 21 million bitcoins? In other words, as the supply of Bitcoin nears its cap, and the reward for verifying transactions is halved, what will incentivize individuals to continue mining Bitcoin if their odds of verifying a transaction before anyone else decreases? And on the off chance that they do it first, the reward will be miniscule. Investopedia touches on this:

In actuality, as the year 2140 approaches, miners will likely spend years receiving rewards that are actually just tiny portions of the final bitcoin to be mined. The dramatic decrease in reward size may mean that the mining process will shift entirely well before the 2140 deadline.

Follow-up question: Couldn't this lead to a monopoly situation where fringe miners give up entirely and only the biggest mining networks reap the profits of continuing to mine Bitcoin?
When that runs out, the system can support transaction fees if needed. 

Satoshi Nakamoto

The fact that the subsidy (newly minted bitcoins) decreases does not mean that the overall reward that miners receive decreases too: they also collect the fee of all transactions they verify and these tend to increase with the use of the bitcoin network.
Furthermore the value of the reward, measured in fiat terms, has compensated the decrease in bitcoins received with the increase in their price (at least so far).

Follow-up question: Couldn't this lead to a monopoly situation where
fringe miners give up entirely and only the biggest mining networks
reap the profits of continuing to mine Bitcoin?

For what we have seen so far, fringe miners are those have high electricity costs or use inefficient hardware, these factors affect more the sustainability of business than the scale of the farms.
It will be always possible run small farms or even a single miner (maybe using an old and cheap asic) if you have near zero energy costs.