Trouble controlling where to add Faces on my model Problem: 
I have a curved edged wire model that I have developed that needs to have a Face applied to it, whilst keeping other "holes" within the model "Face-free". It's like a wire mesh but the wires are much thicker and flat.

How I created it:
I initially used curves to create the model as can be seen below then converted it to a mesh. Then I selected all the edges and pressed "F" to create a face. I hoped that the long flat curved wires would get faces, leaving the middle "holes" empty. Unfortunately only the middle "holes" became Faces and the flat wire sections were left, albeit somehow linked to the middle Hole faces.  

My only other option is to individually select each face in straight groups before pressing "F" but this would take days as the model is pretty large.

Any help would be appreciated.  

Image 1: Pre-Face. I want the thinner parts to have Faces and centre "holes" to be empty.


Image 2: After adding Faces this is the outcome with Faces where I don't want them.


Image 3: After selecting the Hole Face and deleting it the Face icon (the black dot) disappears but there still seems to some form of Face present that is no longer clickable.
The problem is that you're creating one big ngon with that mesh. Blender doesn't work well with ngons and wants tris (three-sided faces) or more preferably, quads (four-sided faces).

Break your mesh down into smaller segments that accommodate Blender's needs. If I were you, I'd just make one big plane and then subdivide it enough that you can form the same mesh by angling rows and columns of vertices to get your desired pattern, and then delete the faces that you don't want. Your mesh pattern is repetitive, so you only really need to create one section of it and then duplicate it as much as you need and merge them all together into a larger mesh.

Here's an example I threw together for you. You can bevel the angled edges to make them more rounded before you duplicate and merge the meshes together into a larger mesh. 

http://www.pasteall.org/blend/42020