Marchita means 'withered', and it's typically used to describe a plant or flower that has dried up. It's a beautifully poetic word you don't often hear in pop songs.
Luis Fonsi creates a powerful image, singing that he has a flower in his pocket that is "marchita de buscar a una mujer" (withered from searching for a woman). This metaphor represents his long and tiring search for love, making the song's core message of 'not giving up' even more moving and hopeful.
Luis Fonsi delivers pure, unyielding romantic hope in "No Me Doy Por Vencido" ("I Don't Give Up"). The narrator starts off keeping totally quiet around the person he loves, comparing himself to a sleeping child who could wake up at the slightest noise: "Soy como un niño dormido / Que puede despertarse / Con apenas sólo un ruido" ["I am like a sleeping child / Who can wake up / With barely a sound"]. He imagines the chaotic moment he finally blurts out his feelings and gets laughed at like a crazy person: "Y te ríes y me tomas por un loco atrevido" ["And you laugh and take me for a crazy, daring guy"]. Even if she thinks he has lost his mind, he refuses to walk away because she has lived in his dreams for so long.
What makes this Latin pop anthem stick is the sheer, stubborn patience at its core. Fonsi uses the vivid image of carrying a withered pocket flower while searching for love: "Tengo una flor de bolsillo / Marchita de buscar a una mujer que me quiera" ["I have a pocket flower / Withered from searching for a woman to love me"]. He believes true joy is only one step away, and his heart kicks up a raging storm whenever he sees her. So he makes a firm promise to wait for a single sigh or sign from destiny, repeating the ultimate vow: "No me canso, no me rindo / No me doy por vencido" ["I don't get tired, I don't surrender / I don't give up"].