Karma doesn't exist in this setting, although Hitokotonushi's predicament is somewhat karmic like you said. Basically, the kami are all in their twilight because the humans' mantra that originally summoned the kami into our physical world had turned into a curse because the humans themselves have grown up and started to recognize the kami as the eldritch otherwordly monstrosities that they were. This created a deadly feedback loop for the kami. Like this chapter describes, the appearance and "being" of the kami is just a representation of the mantra put upon them by their human worshippers. When humans became aware of what kami actually were, the awareness itself reshaped the kami into that negative portrayal humans now had. Humans thought they were scary eldritch beings, so they started turning into exactly that, losing their original selves. This effectively turned the mantra into a malediction for the kami. As the mantra turned into a malediction, it essentially became a cancer that started unmaking the kami in our world. To avoid losing their own mantra, the core of their identities, the kami withdrew from our world.
For the kunitsugami, tied to the land, this meant retreating to the world of the dead, where they could rely on the mantra of their already-dead worshippers who still loved them and saw them as they were in their glory days. Some of them, like Kippuuson (Miyo's ancestral village kami), can sort of cheat through human sacrifice, continually replenishing their "stash" of dead worshippers. Most can't or simply won't.
For the amatsugami, beings from the lofty conceptual dimension, there is more freedom. As manifestations of philosophical concepts, they retreated to their original realm of the philosophical. This is depicted in the manga as something resembling the Platonic realm of forms. In this way, the Amatsugami did not lose their powers like the kunitsugami did.
Hitokotonushi occupied a special place as she was a kunitsugami with the conceptual power of the amatsugami. She was the goddess of words. As such, her powers are conceptual and independent of her worshippers, and she could stay in the human realm longer than the rest of her kin. However, even she isn't free of the malediction. Her current situation, trapped on the moon, is basically a compromise. She is still technically living in the physical world, but is removed from human society in a place where the malediction can't fully unmake her. She is the last real link between the kami and our physical world. Currently she is the only known kami with a physical body other than crowdfunded Shotano'o.