With the 1st feature you sent, I did nothing special in the conversation process. Some things to note:
1) before conversion, the CAD file is an alien format. The import feature gives ability to do some "filtering" in it's native format. That is you can select/contol/modify what's converted
>> change layer colors, visibility
>> change line weights
>> hide/show things
>> etc
2) after conversion, it's no longer a CAD file. Whether or not things are dropped (I didn't notice any). Conversion is an interpretive procedure. There may not be a 1:1 correlation. Visio does its best.
3) the layers, because of (2), migrate to Visio layers. These are now "page" properties. I tested several, and each worked as expected.
HTH