Perfume bottle render creates dark bits even with very high refraction/reflection depth ( 64 )
Testing it in a simple setup, raydepth doesn't seem to have a real effect on the result.
Have you increased the total_ray_depth too? Images would be useful (see right text).
Of course -.-
Total raydepth is 1024 , transparency up to 512 , refelection up to 256 yet I still see black part in the glass , even if I test it with pure white environment color.
Here's an image , I've stripped pretty much everything, this is pure white BG, only the glass, still have lots of black. I've found some ways around but I am unable to reproduce what it does / looks like in real life.
Maybe turn off smooth normals and increase subdivisions? What's the red in your image? Can you try and make your object about unit size and centered at the origin?
Can you upload a scene/.ass file somewhere?