Hello !
After attempting to glue them many times, I have had success using some spray glue from 3M given by my car body repair shop.
The can had no label left (and not much glue left in it) but it did the trick.
I guess that all gluing and cleaning had finally cleaned the slippery out of the rubber. So I'll never know for sure if the glue was special or if the parts only needed proper cleaning...