Can't replicate. What DWG format are you saving to (click on "Setup" button)? I used AutoCAD 2007/2009 and didn't run into a problem. I do get a warning that some features may not be saved in that format, but it does save as a DWG. The Drafting objects (Left & Right views) are there when opened in DWG TrueView.
Designer, Deluxe, (Professional, Expert, Basic), Platinum
Windows 10 Pro (1903), 64-bit