Might be worth sending in the scene :)
Ok got it now, I think! So the opacity of the wave object is being controlled by distance to the "weird shape" object, and where the wave object intersects the square, the wave object opacity of 0 is affecting the green glass of the square, making it invisible. Coplanar faces is my first thought, that the wave object top face is completely in line with the green square top face, thus the engine does not know which material to render and if it renders the wave object, you get this result.
Could also test by just having the wave object with a solid opacity of 0 - it won't render as desired of course, but would isolate whether this is anything to do with the Distance map, or just to do with the opacity of intersecting objects.
Quick solution, just don't have the wave object intersecting the square object at all (slice off the geo of the wave object). Meantime, to explore more, the scene would be helpful, if it turns out that faces are not coplanar :) Thanks!