SolidWorks has an open issue with development to address this. The current workaround is to have the part open at the same time and it should update. The description is "Change to component's custom property, through Assembly Visualization, is not saved unless component is also opened.". The Workaround listed is: "Workaround:Open part file that has property value being added and save."
You are listed in our systems twice, so I'm not sure where I would've sent a direct reply to as your e-mail to us lists "firstname.lastname@example.org".
Fred Zobel | Certified SolidWorks Support Tech
MCAD Technologies, Inc. | 7450 West Alaska Drive | Lakewood | CO | 80226
Phone: (303) 969-8844 x996 | Fax: (303) 969-8855
Can you tell me if this issue has been resolved in SW 2016? I'm having the same problem where the change made to a custom property is not updated at the part level. I would really like to be able to edit everything from the Assembly visualization menu. This would be a lot faster.