Aguante comes from the verb aguantar (to endure, to bear, to put up with). It's a powerful noun that means 'endurance' or 'tolerance', but it carries a strong emotional weight.
In the song, the singer says, "Te agradezco por el aguante" (I thank you for putting up with me). He's not just thanking her for her patience; he's admitting he was difficult and acknowledging that she had to endure a lot to be with him. It's a key word that reveals his deep regret and gratitude.
Julión Álvarez drops all his defenses in this Norteño track, giving us a breakup story where he takes 100% of the blame. Right away, he thanks his ex with "Te agradezco por el aguante" [I thank you for your patience / for putting up with me], using the Mexican Spanish term aguante to acknowledge how much frustration his partner endured. He admits bluntly that she kept asking for basic happiness while he failed to step up: "Soy yo el que no supo amarte" [I am the one who did not know how to love you]. Instead of making excuses, he accepts that he cannot give her what she deserves.
From there, the track becomes a clean farewell wish: "Que te vaya bien" [May it go well for you / I wish you well]. He knows tears are coming ("Sé que lloraré" [I know I will cry]), but he promises to leave her alone entirely, even as his own chest hurts: "Y yo te prometo ya no molestarte / Aunque me duela el corazón" [And I promise not to bother you anymore / Even if my heart hurts]. The final goal is not getting back together; it is simply hoping that one day she grants him her forgiveness ("Me regales tu perdón" [You gift me your forgiveness]). It is honest, a bit painful, and completely self-aware.