How about I add to that. Jake intervenes to stop Rose from being killed with the rest of the Huntsclan, but they all vanish just the same, so it's impossible to tell if he was successful.
Jake wishing that Rose was never taken by the Huntsclan, and could just have a normal life with her family. After a moment, he then destroys the Crystal Skulls before leaving. His scream and tone in how he said to consider the skulls destroyed was filled with anguish, heartbreak and anger.
Lao Shi: If you use the skulls for personal gain— Jake: It won't be for my personal gain! It will be for HER!
Following that up when Jake flies off, Fu Dog and Grandfather Long look down in disappointment or shame at their inability to do anything to help.
And later in the episode, where he finds that this is the case. She doesn't remember who he is, but he asks if they could meet again. She says they can't, because she's moving to Hong Kong. Rather bittersweet, really.
"Half-Baked". After months from the last time they met, Rose appears in Jake's dreams to warn him of the Huntsman planning something horrible. The whole episode is about Jake trying to complete a potion that will create a portal to find and save her... And when he finally got it, he not only has to use it to destroy the source of one of the ingredients, that is the demon involuntarily causing havoc, but when he uses it he accidentally opens a portal to both the demon and Rose, and has to choose between Rose and his duty.
Both the start and the end of "The Hunted". At the start Rose, who has grown to love him, tries and talk to Jake but he, knowing she's Huntsgirl and she doesn't know he's a dragon, avoids her. At the end Rose knows and has passed over the chance to kill Jake, Jake is happy because they can finally stay together... And then he learns she has been transferred.