What a great model, it's simple models that seem to fail like these, that are great to learn from.
My guess is that it is not solidifying because you have left the original surfaces of the solid, delete the back face of the solid first by using Insert -> Face -> Delete...
Then build as usual, until you build the end cap faces.
Lofting a less than 4-sided surface like this is usually discouraged because it causes a degeneracy by collapsing an edge (surfaces like being 4 sided)
You can see this by using Tools -> Sketch Tools -> Face Curves...
You see the U-V flow lines coming to a point and bunching up there, potentially bad situation, although here I don't less than four sided faces with Fill Surface.
This is the default right?
Check off "Optimize Surface" which might as well be called "Make surface awesome".
Solidworks automatically overlays a 4-sided surface and trims back. I believe Solidworks is just about the only software that does this so well!! (not to sound to much like an infomercial here)
Then simply Knit them up "try to form solid" and you're done!
Then, just for kicks, take a look with View -> Display -> Curvature and you'll see it's a nice smooth tangent continuous solid, probably quite good for engineering.
Hope this helped!
Kevin
TDE Technologies
CSWP-Surf