Hi Todd,
Many thanks for posting this issue. By unchecking the “Update Physical Properties on save” checkbox (inside “Applications Options”;”General”), you can avoid this dialog popping-up when you save your part. Also note that this dialog is just a warning message, and will not affect the Save in any way.
As for the mass properties issue itself; unfortunately the accuracy calculation can give erroneous results in certain circumstances, and it seems this model might fit into the category. What I can tell you is that the actual mass property calculations are more reliable than the accuracy calculation, so for a model such as this you can ignore this warning, since the volume, mass, etc. calculations themselves are likely to be accurate.
I don't think the problem is isolated to Inventor 2008; with "Update Physical Properties on save" checked, I can reproduce the same thing in Inventor 2010 SP1. However, work has been done recently to resolve some of these issues, and in my current development build the problem is now fixed on your model.
Apologies for the problems you are experiencing, and thanks again for submitting this.
Jake Fowler
QA Engineer
Autodesk Shape Manager
Jake Fowler
Principal Experience Designer
Fusion 360
Autodesk