Sustente comes from the verb sustentar, meaning to sustain or support. While it can refer to physical support, in this song, it takes on a more abstract and emotional meaning.
Alex Cuba uses it when he sings, "Que el cielo me sustente la razón" (May heaven sustain my reason). Here, he's asking for divine support to maintain his composure and clarity of thought when he finally approaches the person he admires. It's a beautiful and slightly formal word that adds depth to his plea.
Have you ever been so smitten that you completely lose your ability to speak? That's exactly the situation Alex Cuba sings about in "Esta Situación" [This Situation]. He sees someone from afar and admits, "Que tú eres más que un sueño para mí" [That you are more than a dream for me]. He desperately wants to approach them and share all the thoughts he has, but when they look at him, he just freezes up!
He's hoping for a bit of luck and courage from above, wishing that when they're together, he'll find the right words to connect them. But alas, "Si tú me miras se me olvida darle vida a mis palabras, la voz" [If you look at me, I forget to give life to my words, my voice]. He's completely baffled by this feeling, wondering what would happen if they ever said they loved him. He even wonders if he'd stop breathing! He sees this person as his only hope in his loneliness, and their gaze is his essence, their smile his reason to live. He's determined to win their heart, no matter how scary it might be to open up.