The destruction of Kannabi bridge cut off a major supply chain to Iwa's forces, enough to bring Konoha out on top again but not end the war.
Team Minato is immediately disbanded after Obito's funeral. Minato, being a one-man platoon, will only be hindered by two kids, no matter how skilled they are. With his perfected Chidori, Kakashi is best suited for direct offensives, while Rin as a chuunin medic will make the best use of her skills in combat support.
Kakashi is placed with two ex-ANBU who had also just lost their third and sent to the trenches on the front lines. Three miles away, the nearest medical station welcomes Rin with relief — they so severely short-staffed that use of chakra-healing is only allowed for near-death cases. Kakashi and Rin are hardly able to see Minato anymore; his movements have become a S-ranked secret as Konoha presses every advantage they have.
Determined to keep his promise to Obito, Kakashi sends his ninken to watch over Rin on a rotating shift. The plan works surprising well despite the constant, low-level chakra drain it imposes. Seven ninken fight with Kakashi while the eighth takes a day's break ferrying medical supplies between frenzied med-nin. Repeat, rotate. The dogs receive grateful belly-rubs and veritable showers of love. They poof back into the trenches with messages from Rin and bound back with Kakashi's replies, their tails wagging.
Every now and then when there's a lull in the fighting, Sakumo follows the speedy dogs to check up on Rin. Warm pride fill his chest when he sees her working so diligently, level-headed despite each patient's injuries being time bombs. Saving people's lives is a fight just as brutal and unforgiving as that in the front-lines.
The daily back-and-forth is the only respite keeping the both of them sane these days. It's the only breath of fresh air preventing them from suffocating in the pervading stench of blood and death. Amused grins spread across Kakashi's older teammates' tired, blood-speckled faces when the dogs dutifully narrate Rin's messages, which always end along the lines of "hugs, from Rin". Once or twice his teammates are able to drag up enough energy and humour to clap Kakashi on the back and waggle their eyebrows.
When Kakashi sputters comically and turns an deep shade of red, Sakumo can't help but laugh. The silver-haired boy mutters angrily below his breath and he pulls his mask up higher on his face, but never, ever complains to Rin.
The front-line company is regrouping after a hard won fight when Shiba appears, frantic on his paws as he informs Kakashi of Rin's disappearance during an surprise attack by Kirigakure. Sakumo's heart sinks and horror blanches Kakashi's blood-streaked face as he whips around to his teammates.
"I have to go."
His team leader, Naraya, regards him gravely as he leans against the other man supporting him. The stab wound in his side bleeds sluggishly. "We have orders to regroup and report."
"I have to go," Kakashi repeats urgently, the blistered fingers of his right hand clenching and unclenching restlessly.
Naraya's pained grimace deepens as he starts trudging through the undergrowth again. "You know the consequences." His other teammate gives him a sympathetic look.
Kakashi takes the implicit acceptance for what it is and bows deeply. "Naraya-taichou. Kumona-san." Sakumo is sure that Kakashi would have gone anyway, but after months of fighting beside each other, saving and being saved by nothing but the strength they lent each other... Kakashi's absence puts their lives at risk and letting them know is the least he can do.
A second later Kakashi is gone, flashing through the trees as fast as his fatigued body can allow. To conserve chakra, the ninken disappear in small clouds of smoke, leaving only Shiba to track Rin's scent.
Keeping his son in sight, Sakumo follows as closely as he can. A sense of foreboding shivers up his spine and he swallows against the anxiety rising in his throat. They say misery doesn't walk alone*...
* this is my translation of 祸不单行, a Chinese idiom (since I do not know any Japanese idioms). It is probably be a weirdly literal translation, but it sounded poetic in this context so... :)