Go to the Mesh menu and select "Separate Connected Surfaces" to see if that fixes it.
Yep! That did it! Wow. Now that makes me wonder what else this thing does that I don't know about.
What that tells you is you may have issues with the model and need to fix it. In most cases the model should be one mesh.
Try running it through a fixing tool such as makeprintable.com and see if it helps.