There's not always a "reason" to be depressed. Sayori was always mildy depressed, but this depression was extremely amplified by Monika's tampering, causing Sayori to commit suicide. It's also implied that Monika told Sayori to kill herself, however, it's not directly stated within the game
For Yuri, she was always prone to self harm, there is no reason for her to cut, she just does it as a hobby. Again, once Monika amplified her slightly obsessive trait, she became too far gone, and this caused her to kill herself with even the slightest trigger, even if you accept her confession.
However, for Natsuki, there is no real "trait" that could be amplified in her to make her kill herself. Sure, her dad is abusive, but she never has had any thoughts about self harm or suicide, so there is nothing Monika could amplify to make her kill herself, and the easiest way out at that point is to just delete her. People also speculate her neck snapping to be her "death" - even though she comes back a little while after it, and there are a couple theories that state that Natsuki's neck snap had to do with her abusive father.
This shows how great Natsuki's character is: even while her life is not so great compared to others, she still holds on. It's a shame there was so little on Natsuki's backstory in the game, unlike Yuri, Sayori and even Monika.
Monika is stil my favorite though.