#1 Burning Software

I understand that StarBurn supports the Blu-ray format and can burn Blu-ray disks. However, on your features page I find no mention of "3D".

Does your Blu-ray disk burning implementation preserve any 3D video data that might exist... or not?

Have you seen this review?
http://blu-ray-burning-software-review.toptenreviews.com/

Of the many products they tested, only three were known to "Retain 3D Effects".

If StarBurn currently does not do this, are there any plans to support 3D data in a future version?

It's a feature of an authoring and not actually mastering or burning engines. So if you feed "3D-aware" content to StarBurn mastering & burning engine you'll get properly recorded Blu-Ray disc as output.