What has kept the feud between the families going for three generations in the short story, "The Interlopers?"
This is a good question. Since the text does not say explicitly why the feud lasted for so long, we need to infer the reason for the long feud. Based on the text, we can say that there are two reasons for the feud.
First, the land has always been in dispute. According to the text, the courts finally decided in favor of the family of Ulrich von Gradwitz, but the family of Georg Znaeym did not accept it as a just ruling. Therefore, this dispute continued. At this point it is more an issue of personal pride, because the land is not a particularly good tract of land. The text is clear about this point. Hence, the pride of the men stand out. Here is a quote on this point:
The neighbor feud had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to, it was Georg Znaeym, the inheritor of the quarrel and the tireless game snatcher and raider of the disputed border forest.
Second, there is evidence that the two men did not get to know each other. Once the rift took place, there has been little cordial or constructive contact. Within this context, the two men just hated each other more and more. This makes sense, because it is easy to demonize imaginary people. That we are on the right track is confirmed. When the men come face to face under a fallen tree, they quickly reconcile.