Problem with network

 From:  mnrsiat
Hi, I am trying to make a shape using network which seems to me like it ought to be simple... depending on whether I use the small upper circle or not, the command either does nothing, or produces a surface with a big hole in it which you can probably see from the lines, I wasn't expecting. Am I doing something wrong? The help file said it was not necessary for the lines to all be touching as long as they are very close, but it does not specify how close is close enough. Is it possible to make a shape like I'm attempting? The file I am attaching is a simplified version of what I actually want to make, which is a kind of fox ear shape. It lacks the full symmetry of the simplified one but fails in the same way.

thanks for any suggestions!