ZDoom

In the test level I attached, standing on the red square next to the line with the midtexture and looking at it so it takes up the whole screen demonstrates the problem. There's also a set of 8 midtextured lines after that which shows the problem even more. (I go down to 12 fps while looking at that)

This isn't a bug - it's an inherent property of how the software renderer works. It draws all mid textures and sprites back to front which in extreme cases like this one causes a lot of overdraw which slows things down.