Currency failure generally occurs due to the type of hyperinflation, and there is always the potential for technical failure, currency competition, political issues and so on. As the main basic rule, there is no currency that can be considered very safe from failure and difficult times. so is it possible that bitcoin can become worthless?
I don't see any possibility for at least near future. In the near future (10 years) there is no sign it can be worthless. However, we still don't know the real potential of quantum computers, for instance. Quantum computers may compromise the sha256 hash technology. For now, no need to worry about it though.