Supply and demand comes into play here. As a coin becomes rarer and harder to get in the marketplace for whatever reason (and a monopolizer would be just such a reason) the price goes up, making it more expensive for the monopolizer to continue.
But by far the biggest obstacle to the monopolizer is the nature of the coin collector: a percentage of them, at least, want to hold onto their coins because they actually like them, and won't sell them to the monopolizer no matter how much money is being thrown around. The monopolizer will therefore have to outlive and outlast all the hard-core collectors who own one of the coins and refuse to sell, and wait for their collections to come through as estate sales.
As stated above, it's far easier to gain a monopoly at the point of initial release of the coin, the dealer-distributor end. Especially for coins issued under some kind of cozy deal with a coin dealer, as happened several times in the US classic commemoratives, for example, or that guy who pocketed all the surviving (stolen) examples of the 1933 double eagle. And such monopolies are usually founded by coin dealers only temporarily, in order to maximize profits when sold.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis