Hmm... does your monitor go black, or lose signal? If you have a monitor that can display the screen frequency from the On-Screen menus, check that.
There's a monitor file in CyberGraphX (I forget exactly where) that specifies screen frequencies. Perhaps you don't have the proper one set for your monitor, and it is going out of range, hence the monitor can't display anything.
You can most certainly run Workbench in 16 or 24 bit on a CGX3d. I do.
(Also, if you upgraded to CGX4 from a previous version, you may want to go back and make sure ALL files updated properly. (Check version numbers) I ran into a bug like that with mine. Similiar, only I lost all my Amiga chipset generated screens to blackness.)