The tune is somewhat similar to "Go Down, Moses," so the two may be related. The line "sometimes I'm up, sometimes I'm down" is also used in "Nobody Knows the Trouble I See." Jeanette Thompson (soprano) sings "Done Made My Vow" (arr. E. Boatner) in her album Negro Spirituals (Pavane Records ADW 7267), in a slow and mournful way.
Masato