As Romeo is sneaking out of Juliet's bedroom on the morning after their wedding, Juliet has a sort of premonition that they will not see each other again for a long time. She asks Romeo if he thinks they will ever meet again, and he responds, "I doubt it not; and all these woes shall serve / For sweet discourses in our times to come" (3.5.52-53). These lines prove that he feels confident that the two will be together and that all their problems so far will actually serve as the basis for stories they will tell each other when they get old.
In this same interaction, however, Juliet says that she thinks "[she] sees [him], now [he is] so low, / As one dead in the bottom of a tomb" (3.5.55-56). She sees them, in her mind's eye, as somehow forever isolated from one another, despite Romeo's confidence. She sees him now as though he is dead, and they are separated by death (which is, of course, what will happen).
Then, when Juliet goes to the Friar's cell in a panic about her betrothal to Count Paris, she refuses to marry Paris. In fact, she is willing to die, isolated -- it seems -- from Romeo forever: "Be not so long to speak. I long to die / If what thou speak'st speak not of remedy" (4.1.67-68). She cannot abide the idea of being separated irrevocably from Romeo. In fact, at the end of the previous act, she'd said, "If all else fail, myself have power to die" (3.5.255). Juliet's isolation from Romeo and the events that befall her after he's exiled to Mantua make her rather wish for death than a life in which this isolation is continued.