Well, for me, it was a matter that I designed the actual character (the bug like thing) in one program, before exporting to Sketchup and designing it's stand. I made a lot of edits to the model in Sketchup, and everywhere I edited disappeared.
So all I did was have the stand in a Sketchup file, and then import the bug-character, and instead of editing it, just scale it to fit the stand. The scaling doesn't seem to affect the model's integrity, so it worked. I just made sure not to touch the thing.
I've since made a Version 2, which I did by exporting the file with both the DNAVI bug-thing, and the stand, into another program, and then editing it there. Everything worked fine.
I think it's because the two programs I used/use now are both sculpting-based organic modelling programs, which have a lot of polygons, and Sketchup simply couldn't deal with so many polygons when I edited any part of it, causing some bits to disappear. By not editing the Bug inside Sketchup, only scaling it, Sketchup didn't have any issues.
Moral of the story: if you import something with a lot of polygons into Sketchup 8, don't touch it.