Do not, do not, do not watch episode 103 if you've recently moved away. Chi's friend Blackie moves away, and she gets over it fast, in the next episode; she declares "I can't see him, but he's there!" after going through the Five Stages of Grief. Chi's first tears over this are pictured above, after finally realizing that there will be no more "see you later", thanks to a simple open-mouthed smile from Blackie.
Chi's determination to go back home after being separated from her mother can cause some tears. She's also come very close to reuniting with her mother a couple of times but never quite makes it. She does, however, in the final chapters.
There are also hints that Chi's mother and, therefore, her kittens have an owner that might like to know what happened to her lost kitten. It can be very disheartening to see for someone who has lost a pet.