I'm going to have to ask first why you are trying to do this with surfaces. From what I'm seeing, you could easily model this as a solid in SW.
Here you go. The problem was that your sweep didn't follow the exiting edges very well, so there was some weird sliver faces happening. It's really hard to tell unless you zoom in super far.
So then after you delete faces the remaining surface is weird along that edge. Notice how the edge is black and blue instead of just blue. It has that sliver in there too.
To fix it I just unchecked merge result in your sweep to keep it a separate solid body. Then I went through and updated the feature scopes of the features that needed to cut the new body. I edited the delete face feature to include the bottom of the sweep and the top of the base the faces that are touching each other between the two bodies). Then I just updated the relevant edges in the boundary surface. With all that changed the surfaces were able to knit and form a solid.
By the way, you don't need to make those composite curves. In the boundary surface you can use the selection filter to select a combination of edges. When you are making the selections for the boundary surface you can right click, then choose Selection Filter, then pick the option that shows 3 cursors, then select all of the edges that you want included in that single selection, then press ok.
Knitting Challenge JS.SLDPRT.zip 208.6 KB
It is your sweep feature that is messing up your part if you look at your part after the sweep the inside edge is irregular and not made up of a continuous curve see highlighted edges in the picture below
As I am using SW 2014 and you are using an earlier version I cannot send you a repaired file so I will try and explain what I did below
Firstly I edited your sweep feature but instead of selecting your sketches for the guide curve and path I selected the inner and outer edges of the body
This then gave me a continuous curve on the inside edge of the part. To quickly clean up the part where the sweep did not come flush with the end on the left hand side. I did a surface cut using the top plane and then mirrored the part and merged it together again. There is probably other ways to clean up that edge but this is what first came to my mind. I then rolled forward your cuts 5,6 and 7 and made any necessary changes for missing edges, vertices, etc.
I then deleted the faces as you had done and created the boundary surface
Then doing a knit surface I knitted the surfaces and created a solid
Hope this helps