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?
Hyperinflation is the biggest factors that makes currency become worthless. In this case bitcoin is safe because the limitation amount of bitcoin make it tend to deflation. Although deflation of national currency is not always good for economy but since bitcoin is only an alternative currency then it's deflation even give good effects for it's holders. I think bitcoin will not be worthless because currency competition and political issue aren't directly influence bitcoin price.
Bitcoin can still be worthless even the supply is limited. Bitcoin can become worthless if there is no demand in the market of bitcoin because based on the law of demand and supply, the more supply the lower the price. Just imagine no one is buying bitcoin and all of them are just selling then it will end for bitcoin to be worthless.