Problem:
Every time the client edit manually his header in the secondary language, display conditions are lost in both original and secondary language.
Solution:
In that particular case, because the client is editing the secondary language header after the translation has been done it's better to set the translation preferences to "Copy" for display conditions.
- Go to "WPML > Settings > Custom Fields Translation"
- Click "Show system fields"
- Change the translation preferences for the field "_elementor_conditions" to "Copy"