The persistence criteria for branching systems and superprocesses have been established through a variety of ways since Dawson [1977]. We here give an analytic approach to this argument, in which a simple proof of the criteria is available. By extending our result to a larger class of superprocesses with a general branching mechanism, we then get a complete characterization of the long-term behaviour of the superprocesses on the tempered measure space as well as on the finite measure space. Finally, using Dynkin's stopped historical superprocesses, we also show that the extinction and non-extinction of superprocesses at large time are heavily dependent on the branching mechanisms.