Yumemi's eventual fate becomes fairly obvious well in advance, but that didn't reduce its impact when it actually happened.
The line "Why...did everything break...?", as well as the CG of Yumemi's eyes welling up with rainwater, making her look like she's crying.
The last bit of Yumemi's presentation. It makes sense when you realize she's talking about such an optimistic view of mankind colonizing the stars even after all it's done to destroy itself.
Yumemi standing at the entrance on the rooftop endlessly reciting her speech to greet customers that would never come.
In Planetarian Drama CD: Snow Globe, In one of Yumemi's Memory bank, when the Staff members are leaving on an "extended vacation" which happens to be a cover-up for their evacuation, but since they are not allow to bring personal belongings, INCLUDING ROBOTS, they couldn't bring Yumemi with them. The staff members told Yumemi to stay in the Planetarian with "Miss Jena," and Yumemi promised them that she'll do her best here and wait for them, and also that the staff members deserve a vacation for their hardwork. What makes it even more sad is when one of the staff members is crying, kept apologizing to Yumemi many times for leaving her there and wished they bring her with them, but Yumemi remains optimistic and says that robots don't need vacation. 
(Which also counts as a Heartwarming moment) Near the end of Planetarian Drama CD: Hoshi no Hito, when the Stargazer ( who happens to be the Junker in his elder years) starts to reminisce the time he met Yumemi, and slowly starts to dream as his younger self, of walking into the Planetarian, finally filled with customers, and was able to meet Yumemi again, who, despite being a robot, sheds tears with joy for the first time, and the two begins the Planetarian show, and applause were heard... so beautiful ... even what he said during the applause 
Stargazer formerly Junker: Admist the roaring applause, realization dawned upon me. I am but one of the generations of Stargazers, born from this planet and raised by this planet. Now, I too, will join them in the front seats.
What makes it even more sad that the Stargazer passed away, and the three children cried when they heard the news. Trust me, they're not the only ones crying... But at least the Stargazer passed on with a satisfied smile.
In 'Hoshi no Hito,' the Stargazer comes close to finding a robot body to revive Yumemi, but can't because he gave his successors her memory card earlier, and dies soon after realizing it.