Not only should one do anything to avoid machlokes, but if a machlokes has taken hold one should go to great lengths to make peace. The Torah tells us (טז כה) ויקם משה וילך אל דתן ואבירם and Moshe arose, and he went to Dasan and Aviram to try to dissuade them from joining the machlokes. The Gemara says מכאן שאין מקחיקין במקלקת from this we can learn that one should not hold onto a machlokes. Rashi explains that Moshe Rabbeinu went completely against the regular world order. Though he was the leader of the generation and Dasan and Aviram were just commonfolk, he was מחל על כבודו, he overlooked his prestige and did not summon them to him. Instead, he went to them, as if they were equals, in an attempt to douse the flames of fighting.
A remarkable insight is said in the name of Rabbi Shimon Sofer, which seeks to clarify the Gemara's use of the term אין מחזיקין, one should not hold onto a machlokes. It should be completely understandable that one should not hold onto machlokes. In fact, we mentioned earlier that there is an issur against instigating or joining a machlokes, surely it is also prohibited to hold onto an existing feud. He explains that Moshe Rabbeinu did not stay passive in the face of machlokes. He had three earlier interactions with Dasan and Aviram, and all proved that they were not particularly inclined to follow daas Torah, and they were highly unlikely to take his words to heart. Still, he attempted to persuade them of the folly of this feud.
He could have relied on the halachic ruling of chazakah, that if something has occurred three times, it can reasonably be expected to reoccur. However, he did everything in his power to attempt to resolve the argument. אין מחזיקין במקלקת even when he could have relied on earlier precedents, he still did everything in his capacity not to hold onto a machlokes. (עולמו של אבא ע' שכ).