If none of the other solutions work for you, try to delete the entire technicssp folder located in %appdata%/.techniclauncher
I had the exact problem, "Update Failed!", and it turned out I apparently had corrupted files in my technicssp folder. The Technic Launcher couldn't update, because the files couldn't be removed. I had to run Chkdsk to fix it, because some of the files were corrupted.
This wasn't the Technic Launcher's fault, nor the mod maker's fault. It was mine alone.