Well,
Considering that we lower our flags for;
National abused women day, tsunamis, floods, hurricanes, the anniversaries of the Montreal Polytechnique massacre, 9/11, and others, a soldiers death should be national if on operations, and local if off duty.
I think we lower our flags for far too many things already though.
I heard a funny story about this though!
When Sheila Copps was the Heritage Minister, she decreed that the national day of abused women to be a national day of mourning, and all flags would be at half mast. The following year, she was in the presence of a Naval vessel, and observed it to be flying the Canadian flag at (full?) mast. So she demanded it be lowered. The Captain of the ship himself spoke to her and made it known that a flag at half mast was an international symbol of distress (or some other sign of "assistance required") She would not budge though, and ever since, Canadian ships are plagued with offers of assistance whenever they go to sea on on of our many days of mourning.
Can anyone in the Navy authenticate this?