My wife is suffering from excessive hair
loss, and it was suggested to her that she should cut her hair short to reduce this loss.
Is this permissible?

Praise be to Allaah.

If this is the case, then it is permissible to cut her hair
because this will protect her from harm. (Fataawa al-Lajnah al-Daa’imah,
5/182), on the condition that she should not make herself look like men or kaafir
women. See Question #1192. And Allaah
knows best.