Contentarla comes from the verb contentar, meaning "to make someone happy" or "to appease them." It's a less common verb than hacer feliz and carries a nuance of soothing or satisfying someone who is upset.
In the song, the singer laments, "Ella está triste y no creo que poder contentarla" (She is sad and I don't think I can make her happy/appease her). This word highlights his desperation and the difficulty he faces in trying to mend the relationship after repeatedly failing her.
This song feels like listening in on the exact moment a relationship finally breaks after too many chances. The singer looks at her and repeats "Ella está triste" ["She is sad"], but he knows it is not some mystery feeling. He admits she is tired of fighting to keep them together, tired of forgiving him and watching him mess up again: "Parece que está cansada de luchar / De perdonarme y que le vuelva a fallar" ["She seems tired of fighting / Of forgiving me and me failing her again"]. By the time he notices how serious it is, it is already over. When he tries to hug her, "quiso abrazarla y nomás no se dejó" ["I tried to hug her and she just did not let me"], and that cold distance hits harder than any shouted argument.
What makes it hit even more is how clearly he blames himself. He is not pretending it was bad luck. He says she gave him "como 10 chances" ["like 10 chances"], and every time he just "vuelvo a regarla" ["mess it up again"]. Now he has to watch her cry "a causa de mis errores" ["because of my mistakes"], and he knows there is no fix this time. She will not even listen to him: "no me quiere ni escuchar" ["she does not even want to hear me"], and he repeats that she will not forgive him anymore, no matter what he does. When he admits "Y es por mi maldita culpa" ["And it is my damn fault"], it is blunt, almost harsh, but that honesty is what makes the song feel so direct: it is a guy finally realizing too late that sorry is not enough when you keep repeating the same mistake.