So many possibilities on this one, it may be too hard to explain via forum without seeing your model.
1) Is the model hidden?
2) Do you have Occurence Properties set to not show in higher level assemblies?
3) Is it a valid solid (water tight) and not construction geometry?
4) Are you using Display Configurations?
Those are 4 areas just off the time of my head that you need to check.
It's the part copies that are the issue. They are most likely NOT water tight solids. They have some bad geometry or are only surface bodies that look water tight.
Two ways to check:
1) Open up each of the troublesome part files and make sure you assign a material (density) and update the physical properties.
2) Do you have the option to run the OPTIMIZE command on the part files?
Appears your parts are made of construction surfaces as Scott surmises. RMB on AmsB and run "Show/Hide Component..." which lets you control display of elements within components. On the dialog, check "Surfaces" ON and Ok. This should turn on all construction geometry in the parts.
If this shows the geometry as you expect, you will need to turn these constructions into solid design models. If it does not, you might want to post your test data here or call in an IR.
You seem to be running an older version of SE (pre-ST6?) before the show/hide component command existed. As a test in your version, select a few part components and turn on Surfaces.