I heard about others having problems with the lens hood for the FE 35 f/2.8.
Now it happened to me also , even if i treated the camera/lense with care.
The hood is made of two parts "glued" together with a sticky substance that seamed to have low or no
adhesion , just like cewing gum. It is to expect that a product like this can withstand normal use.
Maybe the lenshood should have been made i one part , it's not impossible for sure.
I myself have fixed the lenshood by gluing it together with superglue inteded for that kind of materials ,and now it seems to be OK .