The half lives of many radioactive nuclei can be determined with high precision

The problem with radioactive materials is that they are continually shooting out subatomic particles (that changes their mass slightly), and the fact that they are radioactive makes them a bit hazardous to handle, and could affect the operation of nearby electronics making the measurement.

You can't easily average measurements made on 10 successive days, because the decay rate will differ on every day.

While the original element may be quite stable, fission decay products are sometimes a bit unpredictable, and some of them may react with oxygen in the air.

There has been debate for some time about redefining the SI kilogram.

One of the proposals was to base the kilogram on a certain number of atoms of isotopically pure silicon. So various teams produced highly-polished silicon spheres, and then attempted to count the atoms, by various methods. This would have defined Avogadro's number in a new way.

For some of the saga, see:

http://spectrum.ieee.org/consumer-electronics/standards/the-kilogram-reinvented However, the current recommendation is to define the kilogram in terms of Plank's constant. This in turn will in turn produce a more traceable value for Avogadro's number.

See:

http://en.wikipedia.org/wiki/Proposed_redefinition_of_SI_base_units#Kilogram