Bissonomy is the virtue of stability.

Specifically, bissonomy is the virtue of knowing (-nomy) how to attach yourself ("bissys" is the name for filaments by which certain bivalves attach themselves to rocks and other substrate) to some stable object.

Arguments:

• The name. It basically tells you outright (and "bisso" is Portuguese for "bissys", just in case).
• She was turned into oysters -- bivalves -- which is a big hint.
• She was punished for throwing a mole. What do moles do? They dig! They undermine and clearly, the virtue of stability couldn't be seen undermining anything.
• Two children is another hint at stability as families with two children neither increase nor decrease the population -- they keep it stable.
• She was forgotten -- for the only thing constant in the world is change.