Why and how did Valentine disappear?

I think Valentine's disappearance is open to interpretation, which of course depends on how you viewed her character throughout the film. My thoughts are that Valentine was so much more than just Maria's PA, which is why she couldn't see it through to the end; the frustration was too great. Valentine desperately wants Maria to see that she represents a timeless actress (I liked how that was mirrored by the young directors' offer towards the end of film) but Maria only seems to be able to focus on the time that has passed. Valentine said herself that Maria could've had anyone there to run lines with her, that she could only stay if she felt able to offer her opinion and her interpretation on things; this proved impossible as the two women had crossed words yet again on the mountain. I feel this spurred Valentine to simply leave because she knew that Maria would never actually let her go, but their separation was needed so that each person (especially Maria) could grow in the way they were supposed to. Again, I enjoy the part at the end with the young director pitching his idea to Maria; it reconfirms that she's still seemingly anxious of her age and so tries to give away the part to her younger co-star, but the fact that she even met with the director for a film that would've been classed as 'sci-fi' meant that Maria was actually listening to and valuing Valentine's opinions all along.

Valentine left for two reasons...she was fed up with it all and to prove her latest character point to Maria. Keep in mind she had just argued with Maria (as they hiked up the mountain) about the presumed suicidal outcome of poor Helen. Maria insists that when the distraught Helen does not return from her hike, it is because she has killed herself over Sigrid leaving her. Valentine tries to explain that Helen might not have ended her life, maybe she just walked away from it all and reinvented herself. The original play is not clear as to whatever became of Helen. It supposedly is left up to the viewer to make their own decision regarding Helen's demise! Valentine, choosing to walk away from Maria and reinvent herself, was to prove that point!

Valentine tells us she is leaving the older actrice one day, in her lines. it It is so that the great actrice won't be controlled by Valentine...their view points about the theatre character have become a contention between the employee and employer. Watch the movie again and pay attention to the words Valentine speaks. Now these words can be taken many ways...1. as nothing more than lines in a play...or 2. as real words spoken from a young woman (who recognizes her power) to an older woman (who is feeling powerless) 3. because Valentine is pregnant (she throws up) 4. She disappears because she is dying of a form of of cancer (and under kemo which makes a person throw up). But of these many choices I believe Valentine disappears one day because she gets the idea to do this from the actual lines of the play she is assisting the actrice with during their roll playing...so, in the mountains one day she simply walks away... so in her estimation she is releasing the actrice from all control Valentine may have over her so the famous older actrice can go into "timelessness". ...Valentine left (like she said she would) to help the situation.

There are so many beautiful interpretations. Here is one:

Valentine leaves Maria just like Sigrid leaves Helena in theater, leaving Maria alone in the mountains. Yet in real life, in contrast to the theater where the audience is focused on Sigrid, we are focused on future of Maria (Helena). Recall the words of Valentine who said that Sigrid's leave would help Helena to re-invent herself. And we indeed see that Maria changes afterwards: in the last scene, Maria accepts the role in sci-fi movie she would not accept before Valentine left her.

(Also fun note: Observe that Maria asked Valentine not to leave her, how Maria became dependent on Valentine, how their relationships were developing and mixing the theater with reality. They were Sigrid and Helena of real life. And it is not that clear who is Sigrid and who is Helena, i.e. who used whom, and who benefited more.)

See also interesting interpretation and discussion here: https://www.thisisbarry.com/film/clouds-of-sils-maria-2013-explained-what-happened-to-valentine/