This question can be answered based on Rashi's understanding of Bamidbar 14:36, which addresses a similar question: Why didn't Moshe's prayer help the Spies as it helped the entire Jewish people when Hashem wanted to "strike them with pestilence and disown them"?
וְהָ֣אֲנָשִׁ֔ים אֲשֶׁר־שָׁלַ֥ח מֹשֶׁ֖ה לָת֣וּר אֶת־הָאָ֑רֶץ וַיָּשֻׁ֗בוּ וילונו [וַיַּלִּ֤ינוּ] עָלָיו֙ אֶת־כָּל־הָ֣עֵדָ֔ה לְהוֹצִ֥יא דִבָּ֖ה עַל־הָאָֽרֶץ
As for the men whom Moses sent to scout the land, those who came back and caused the whole community to mutter against him by spreading calumnies about the land
Rashi on the verse explains why if their sin was complaining to Hashem (“How much longer shall that wicked community keep muttering against Me?" 14:27) does the verse mentions "muttering on him" (וילינו עליו) which is referring to Moshe.
So Rashi explains that the verse is coming to teach us why only the spys died and were not helped by Moshe's prayer. They intended to to "complain against him" against Moshe himself. Therefore, Moshe's prayer did not help them: אין קטיגור נעשה סניגור-a prosecutor cannot become a defendant, and Hashem judges a person מדה כנגד מדה.
וישבו וילינו עליו. וּכְשֶׁשָּׁבוּ מִתּוּר הָאָרֶץ הִרְעִימוּ עָלָיו אֶת כָּל הָעֵדָה בְּהוֹצָאַת דִּבָּה אוֹתָם אֲנָשִׁים
AND THEY RETURNED AND MUTTERED ON HIM: This meant: “the men whom Moses sent and who, when they returned (וישבו) from searching the Land, made the whole congregation murmur against him by making them utter an evil report, — those men died.
Therefore, it is understood why specifically Korach and his congregation died, and why Hashem "took off his gloves": Korach and his congregation attacked Moshe. Thus, there was no one that was on Moshe's caliber to pray for them and save them from G-ds anger as Moshe did so many times; Moshe couldn't because אין קטיגור נעשה סניגור. Another reason is מדה כנגד מדה because they fought Moshe they don't get Moshe's help.
All of this is based on Likkutei Sichos and footnote 29* there. See there for a more complete explanation as this was just a very short summary.