Desvelos refers to sleepless nights or wakefulness, often due to worry, love, or deep thought. It's a more poetic and intense word than simply saying "no puedo dormir" (I can't sleep).
In "Triste Recuerdo," the singer repeatedly mentions "en mis locos desvelos le pido a Dios que vuelvas" (in my crazy sleepless nights, I ask God for you to return). This word beautifully conveys the depth of their longing and the emotional turmoil that keeps them awake, making it a powerful and memorable choice.
"Triste Recuerdo" ("Sad Memory") is about someone who can't stop thinking about a past love, no matter how much time passes.
The lonely nights only make the longing worse, and every attempt to move on fails - the memory of this person stays constant.
In the chorus, the narrator admits they still love this person and hopes that, wherever they are, they'll hear this song and think of the narrator exactly as often as the narrator thinks of them.