Even though I run the game through Steam, I play on the non-Steam version of Warframe, for reasons best explained elsewhere. Anyhow, the title of this post basically says it all: the L1/LB button doesn't move the player down in "flying" type gameplay like it should. My temporary fix was this:
With a 5ms delay on the "Left Bumper". Not an ideal fix, as it makes navigating menus flaky, but it works for now.