Cutting hair because of sickness

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 Allah, and blessings and peace be upon the Messenger of Allah:

If this is the case, then it is permissible to cut her hair because this will protect her from harm. (Fatawa 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 Allah knows best.