Listen to Don't Fall Asleep online. Don't Fall Asleep is an English language song and is sung by Artie Shaw And His Orchestra. Don't Fall Asleep, from the album Gloomy Sunday (The Bluebird Recordings in Chronological Order, Vol. 6 - 1939 - 1940), was released in the year 2013. The duration of the song is 2:55. Download English songs online from JioSaavn.