Why does the Canterville ghost remain unseen for a long time?
I believe that this question is referring to events that occur in section four of the story. Up to this point, Sir Simon has been putting forth a valiant effort to scare the Otis family. Unfortunately for Sir Simon, all of his attempts have met with failure. Not only is the Otis family not scared of him, but they treat him like he's a joke. The twins are especially antagonistic to Sir Simon, and they play all kinds of pranks on him. By section four, Sir Simon is tired of dealing with the Otis family, and he is even a bit scared of them. He resolves to stay hidden for a bit.
The next day the ghost was very weak and tired. The terrible excitement of the last four weeks was beginning to have its effect. His nerves were completely shattered, and he started at the slightest noise. For five days he kept his room, and at last made up his mind to give up the point of the blood-stain on the library floor.
Sir Simon might have stayed hidden for longer than five days, but the narrator tells readers that he has ghostly duties that must be kept up on a regular schedule; however, Sir Simon resolves to be as stealthy as possible during his haunting.
For the next three Saturdays, accordingly, he traversed the corridor as usual between midnight and three o’clock, taking every possible precaution against being either heard or seen. He removed his boots, trod as lightly as possible on the old worm-eaten boards, wore a large black velvet cloak, and was careful to use the Rising Sun Lubricator for oiling his chains.
The Otis children catch on to Sir Simon's new tactics, and they continue to antagonize him. They are able to make a bucket of water fall on him and even manage to scare him by jumping around a corner and yelling "BOO!" Sir Simon is so frightened by this last encounter that he gives up his haunting completely.
After this he was not seen again on any nocturnal expedition.
The Otis family is so certain that Sir Simon is gone that Mr. Otis writes a letter to Lord Canterville that states the ghost is gone.
It was generally assumed that the ghost had gone away, and, in fact, Mr. Otis wrote a letter to that effect to Lord Canterville, who, in reply, expressed his great pleasure at the news, and sent his best congratulations to the Minister’s worthy wife.
In Chapter Four, the Canterville ghost decides to remain unseen by the Otis family. This is because he feels "weak" and "tired" after four weeks of trying to scare the family. All of his attempts so far have failed and he has been thwarted by the family, especially the twins, at every turn.
In this chapter, he has one final attempt at scaring the twins while dressed in one of his most famous disguises, "Jonas the Graveless." As he goes towards the library, however, he is met by "two dark figures" who wave their arms wildly above their heads while shouting "boo" at the ghost. As he flees, he is met by Washington Otis who is lying in wait with a "garden syringe." Luckily, the ghost is able to vanish into an unlit stove before any more damage is done.
Now described as an "invalid," the ghost is so terrified of the family that he is incapable of leaving his room, even when he comes up with a plan to scare the young Duke of Cheshire. The family think that the ghost has voluntarily left the house; they have no idea that he is deliberately hiding away for fear of meeting them again.