This is something that is not necessarily highlighted in the text, so I can understand your confusion over this issue. The section you want to look at is when Marlow overhears a conversation between the uncle and his nephew as he wakes up from a nap in the boat one day. They, not knowing that he is nearby, are speaking freely about somebody who Marlow comes to realise is Kurtz. Note what they say:
"The climate may do away with this difficulty for you. Is he alone there?" "Yes," answered the manager...
The only other news or sign of Kurtz's continued existence is the massive quantities of ivory that he has gained through his domination of the tribes around his station. This, according to the nephew, is "most annoying, from him"
From these clues we can piece together the scenario. Kurtz is seen as a threat to the nephew and his uncle, who clearly resent the power and influence and success that he has gained through his skill at obtaining lots of ivory, which was of course a very wealthy commodity. They therefore stop Marlow from repairing the steamer for as long as possible in the hope that Kurtz will succumb to some kind of illness and that this will "do away with this difficulty" for the nephew and leave him to gain the power from the vacuum that Kurtz will leave behind him.