In SW2016 when you save a mirrored part (or any referenced part for that matter) and fill in properties using the custom properties tab, they disappear after saving and reopening. However, if you fill out the values in the regular properties form, they stay.
PDF after initial save
Re-opened the part. Note that it is a "save bodies" part, but mirrored parts do the same thing. Has this been fixed in newer versions of SW? Trying to decide if it's time to upgrade.