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?
Maybe you're one of the people who had once high expectation on bitcoin to flourish in just a short period of time. But, knowing bitcoin's current situation, bitcoin still has a lot to develop. This might be the reason why you have doubt in bitcoin's capability. What you should keep in mind, bitcoin is a young technology that as of now shows great potential and also great conflicts in government's interest. Through time, this technology brought by bitcoin will soon be recognized fully.