Might Duy, Shinnosuke, and Hikari's three-man squad did not march out with the main army this time. Instead, they were kept at Konoha headquarters by the higher-ups.
With Konoha's Kage-level fighters now mostly deployed outside, only veteran Kage-level powerhouses like the Third Hokage remained to hold the fort. Yet the four of them were Konoha's highest-ranking decision-makers. If an exceptional situation arose and they had to take the field personally, it would not only be beneath their status but also dangerous. Should any one of them die unexpectedly, Konoha's political situation could easily be thrown into turmoil. Thus, the higher-ups deliberately kept Might Duy, a newly promoted Kage-level fighter, at headquarters as one of Konoha's trump cards. Shinnosuke and Hikari, his teammates and both elite jonin, were naturally kept behind as well.
In truth, aside from those reasons, Konoha's higher-ups had selfish motives of their own. Nawaki's faction had become far too powerful. They alone had ten Kage-level fighters, while Tsunade, Jiraiya, and White Fang had already risen to positions of real authority at the ministerial level. Had Orochimaru not "betrayed" them and joined Danzo's camp, the older generation of powerhouses would likely have been unable to keep Nawaki's faction in check much longer.
Might Duy was Nawaki's eldest disciple and a Kage-level fighter himself. If he had marched out with them, then given Nawaki's protective nature, he would certainly have helped his disciple earn great merit. That would have further strengthened Nawaki's faction politically, and more importantly, Konoha no longer had any positions left with which to reward them.
So they simply found an excuse to keep Might Duy at headquarters, preventing him from winning merit on the battlefield. At the same time, they could try to use Shinnosuke's connection to win him over. It was impossible to make