I think a lot of different reasons, first if the melody is slow and depressing, that can get you down. My ex would sing some songs to me, so every time I heard those songs I remembered him singing them with his guitar to me. ( so that example would be connected to memories ) A lot of songs are connected to experiences.
Because they can relate and it brings back old feelings? Would you get depressed if your mother died and I repeatedly phoned you and said 'Your mother has passed away. You're going to miss her forever. Your mum is DEAD' each time I phoned?
Cause in some way they can relate either they have had a bad break up or are so in love, or they are so in love that they fear they may lose that person.
Perhaps similar things have happened to them, and hear the songs, and the emotion in the song brings back memories of it.
for me it makes me remeber the past and all my own releastionships and how i lost friends and stuff
because they probely had a sad point in their life an sad songs make them renember those time x :D
Maybe because it reminds them of their past