Unlinking a support or effect by dragging it to the main system column doesn't add that one to the list till you re-open the weapons menu.
There are some exceptions to that though:
- if you unlink for example 2 or more of the same system in a row (example 2 damage beam computers used as support),it will add the 2nd, 3rd, ... one to the list properly. It's just the 1st one you unlinked that won't appear.
- if you link the same support type as the main one, it always re-appears properly. A cannon + cannon weapon when unlinking the cannon will appear properly.
The list seems to refresh every time when you unlink but the item that was unlinked doesn't always get set properly to be included into the main list before it does the refresh.