Why is Canada unable to prove its Arctic sovereignty?

For two very good, more detailed explanations of this
problem for Canada, please follow the links below.

There
are two major problems with Canada's claim to sovereignty over the Arctic.  First, there
are physical/geographic issues.  Canada has to prove that the waters between its Arctic
islands are "internal" waters (not open sea like, for example, the ocean between the US
mainland and Hawaii). In addition, it has to show that those waters are not "used for
international navigation."  Both of these are not easy to
do.

Second, there is also the issue of what Canada has and
has not been doing to stake its claim.  Canada has typically failed to patrol the waters
that they claim.  This is a problem because countries are supposed to patrol areas that
belong to them.  The issue here is whether Canada has done enough with the Arctic to
uphold its claim.