Comedy or anything relevant to comedy that has lost its comedic value or never had any to begin with is termed as dead comedy.
Overusing a joke or milking a concept to the extent of it becoming oversaturated can lead to dead comedy. Dead comedy can also occur if something of comedic purposes is initially forced, basically a real bad joke.
Once something has been categorised as dead comedy there is no going back, it's permanent. If you're uncertain whether something is dead comedy or not, chances are that it isn't. If so, it's in a state of limbo, it needs a push in either direction for its fate to be sealed.
Synonyms: Random unfunny
Steve: "Hey, Jack. Have you seen the latest Family Guy? It was funny as hell!"
Jack: "No, I don't watch dead comedy."