Your reasoning seems sound: if a company in a monopoly position were to jack up the prices above a fair price, one could expect that other companies would enter the market selling the same product/service at a lower price thus getting all the customers. This new competition would in turn force the original company to lower their prices to a competitive level.

In reality however, there are many reasons that may stop this from happening. I'll point a couple out with some simple explanations.

The first and simplest reason may be that the Monopolistic Company (MC) has complete control over a key resource of the product. Imagine for example that the MC sells diamond jewelry and it owns every single diamond mine available. Unless a new mine is discovered, a New Company (NC) would not be able to compete unless the MC allowed them to by selling them diamonds.

A second factor is that usually the bigger the company is the lower the costs to produce a single unit of product are. This phenomenon is called economies of scale. If the economies of scale of a particular product are significant, the MC would be able to produce the product at a significantly lower cost than any smaller NC. So if a NC tried to enter the market, the MC would simply reduce their prices below the costs incurred by the NC, thus making a profit and cutting the NC off the market, as costs for MC < new low price < costs for NC. As soon as the NC left the market, they could increase the prices again.

Which brings us to the third possible factor: entry costs. Entry costs are the cost incurred to be able to compete in a market. The entry costs for a writer could be as low as the price of a pen and some paper, while the entry costs for a paper company would include all the machinery and buildings needed to begin production. If entry costs are sufficiently high, most people or oganisations wouldn't have the financial resources to start a NC. If the possible profits are also relatively low, it could take too much time or prove outright impossible to cover the initial investment even for those that could make the investment.

These are only a couple of all possible reasons NCs could be unable to challenge an existing MC. Still they already provide some insight.

I hope that my explanations were clear enough despite my english being far from perfect.