Hi Stefan,
Which exact version and hotfix do you use? If it is version 7 and you do not have the latest hotfix applied, please do so since there were several bugs related to "Multiple Category Selector" form control which might cause the issue you experience.
However, I tested it with the latest hotfix (7.0.76) and the same scenario as you described worked just fine for me, i.e. selected categories in Form tab were saved and displayed in Properties -> Categories correctly.
Best regards,
Filip Ligac