I'm not sure about the best way to translate "that will never work" and similar phrases with a vague "that" as the subject (like "that's not a good idea" or "that's the third time he said it"). Should I just leave the subject off ("no va a funcionar")?
"That will never work" can be translated as:
Eso nunca funcionará (That will never work).
Eso nunca va a funcionar (That is never going to work)
The other sentences you listed can be similarly translated as:
Eso no es una buena idea (That is not a good idea).
Esa es la tercera vez que él lo dijo (That is the third time he said it).
You can omit the "Eso" (that) as you have done and the sentence will still be correct, provided it is clear what "that" refers to.