So to get back on topic....
I think that Buffy's depressive moments in life are an important part of the series, and what has made some of it so relatable to me. I think it's safe to say that Buffy doesn't have an "easy" life in the series. Life is not pure optimism. It's not perfect. It's marred by sadness and depression. Life has its ups and downs. I, for one, would find it hard to relate to someone who faces as many hardships as Buffy does through the series and doesn't get down from time to time. Buffy mourning the end of relationships just shows what happens in real life. Most of the time, breakups make people sad. That's how it is. Buffy takes the time to mourn the loss of something and someone important in her life, and moves on. I think this is the important aspect that gets lost in the "oh Buffy's just off moping again" view. She lives, loses, mourns, learns, and moves on. She goes through the entire gauntlet of human emotions. And really, if my boyfriend started killing my friends or up and left on a military mission without a look back, I'd be kinda sad too.
Life isn't all roses and ponies. It's hard. And for some, it's a lot harder than others. I'm not going to pretend that I've had it as hard as some in this world, but I've been through the ringer a time or two and for me, seeing a character that I look up to like Buffy and being able to relate to that sadness inside helped me cope with things. I've gone through bad breakups. I've lost several loved ones. I've dealt with divorce and addiction in my family and with friends, and I've gotten sad over these things. I still struggle from time to time to always see the bright side. Does that mean I quit trying just because I'm upset? No. Buffy doesn't quit either. She doesn't give up, but manages to work through a gambit of emotions. But she doesn't remain unscathed either.
Experiences in life change us, for the positive or negative. We learn from them and we grow and move on. But that doesn't mean we can't be sad or upset over them. Buffy can't be a relatable character and break up with someone and go "oh, well that's alright. I'm good." It wouldn't be realistic. While the show speaks in metaphors, it very much deals with real human emotion and human experiences, and sadness and depression are a part of life.
I do think our society in general does have a bit too much of "wah, I'm a teen and I got a volvo instead of a mercedes for my 16th birthday, my life sucks" in it, especially in our entertainment industries. But that doesn't mean that there also isn't a place for expressing true human emotions, including sadness. One of my favorite bands (Everclear) often addresses life altering events that caused exteme emotional turmoil through their music. And it's a beautiful thing. It's sad and poignant and beautiful because it is real and human. Life isn't dasies. Life is tough. Buffy goes through the hard times and isn't unaffected and unmarred through her trials and tribulations, and I for one find this to be a great thing because of the way it is portrayed in the series. If Buffy was whining because she had "last month's hair" ALL the time it'd be one thing. But to be sad over major things in life like relationships? I'd call that a pretty accurate depiction of a real, relatable character.
Ramble over.