Discontinuity is by far the most likely course for a character, even once they pass that dangerous threshold of the first level and manage to get some experience under their belts. There are endless opportunities to die and the law of averages states that the longer a PC pushes his adventuring career the more likely it is to end in sorrow. The tragic death (for in this example all deaths, whether filled with poignant dramatic irony or not, are tragic) of a PC completes the arc -- unless they are returned from the grave, but we all know that I personally believe that cheapens the very meaning of death itself unless it is rare, difficult, and grim.
This is one of the two binary options for PCs in D&D. If you play a character for long enough, no matter your intentions, you will reach death unless you somehow become immortal. You know what they say, on a long enough timeline everyone's survival rate drops to zero. That means that the ultimate tragedy lurking beneath D&D is one of discontinuity, the interruption of life and the shattering effects of death, right?
Well, no. There's always the option of retirement. Retirement can come at any level and is a way to integrate your character permanently into the setting in which you play. Even if time progresses and the retired character eventually dies outside of your control, a good DM will allow the setting to change and reflect the influence of the retired character (particularly if they are high level or have a powerful or influential family). Retirement, then, is the ultimate expression of continuity, and serves as a type of campaign building. After all, retired characters have probably conquered great evils and become productive members of their society, particularly if they've founded huge fortresses or become lords or any of that.
Death is the poorer of the two choices, cutting characters from the fabric of the setting completely. Yet, even then, it need not be so sharp (and death may retain its sting). For example, recently (last night) Crispus (Felix Flavius by an assumed name) died while crossing a lightning trap. This would at first appear to be the ultimate discontinuity as a representation of death in a game. However, he was also an important member of the Cult of Aros and a servant of that god in many of his actions.
His spirit, which lives on in the 10th Age, has been taken to Aros' bosom amongst the Garden of Winds to join the hosts of the Wind Lord. Even though Crispus is dead, he is ultimately not gone. While he may not be available to influence the world of the living in most cases, he still exists in the realm of Aros and can potentially be called upon as a powerful spirit in the future. He exists, just not here.