Hi Bluelinner,
Your Pieris japonica aka Andromeda could have a pest called nematodes that live in the soil. They destroy the roots and the plant begins to wilt and die. Phytophthora root rot is another possibility. Try digging around the root system to see what you find.
They can also be attacked by mites. If you don't see webs, just put a piece of white paper beneath some limbs and tap the plant to see if any tiny specks drop on the paper and move around. The can also get scale insects or lacebug, but you should see these on the branches.
http://www.onlinegardener.com/trees/Pieris.pdf
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.