I am having an issue with the knife tool. I'm attempting to make a cut where the maroon line is in the above image, however, when i click the left mouse button, the line goes away, and no cut is made. Please let me know if you have any suggestions or need additional information, I appreciate it.
The reason you're having the issue is because there's no face there to subdivide.
Editing in Solid Shading often makes things like this difficult to see. Faces will always have a little black dot in the center, though.
Go to edge selection, hold Alt and click one of the edges surrounding the void then press F to fill the face.
After that, the knife tool will work as expected.