Hendryk really hits on the key point, there isn't just one China that Japan has to make peace with, its two. On the one hand, it would benefit Chiang to just get the Japanese off his back so he could deal with Mao. Worthy of note is that he largely ignored Japanese encroachments into Manchuria in favor of trying to exterminate the communists; not to say that he didn't care, but its a matter of priorities. However, as mentioned previously, any capitulation on Chiang's part is only going to strengthen Mao, something he also does not want. Further, Chiang is no position to negotiate and Japan possesses little impetus to seek any settlement but their own: the domination of China. In order for the Japanese to seek any other settlement the Chinese have to beat them back first, something which Chiang cannot accomplish on his own. He needs Mao to fight Japan, and Mao is not going to accept a settlement because in the larger scheme Mao only benefits from that fight. Beyond this, it also assumes that the CCP and KMT together could put the Japanese back on their heels, something which they weren't very successful at OTL.
So, you need to get Mao and Chiang in the same boat, get them to together beat back the Japanese, and then get them to together accept a settlement with Japan. These are some tall orders. Even knocked back from their main line of conquest, Japan isn't going to let go of Manchuria, plain and simple. This is something which Chiang might accept for the time being, but Mao has less to lose and more to gain and will likely act as a spoiler. Even if at this point Chiang chooses to break the United Front (again), make a separate peace with Japan, and resume going after Mao, he will have suffered a huge propaganda defeat in doing so, as we've discussed.
The long and short of it is, without some prior PoD and more significant butterflies, nobody in this scenario has any great motivation to seek peace.