The key reason one don't lose sense of depth is because of monocular cue. Our brain can still detect the actual position of the object with helps of cues even if one eye is closed.
Such cues include (but are not limited to):
Linear perspective - the fact that additional objects ultimately travel to a single point (i.e. two roads that converge into a single point in the distance)
Texture - objects closer to you will have more complex texture compared to objects further away from
Interposition - objects closer to you will be farther away from objects
Accommodation - as you look closely at items, your eyes need to accommodate and concentrate on them using your eye muscles, giving your eyes an idea of where the object is located.
Hence, Monocular Cues are used by using one eye to help sense distance.
