I think of this in terms of entire shows or series often. Someone decides to make a sequel and I think: this already had a fantastic ending... why take a chance and put out something that might not be as solid. On the other hand, I've seen a lot of sequels on par with or surpassing their predecessors.
Honestly, it kind of depends on where the character was going. Sometimes, the story for that character leads naturally to a death sequence. For instance: anything remotely military faces mortality all the time, or a self-destructive character destined to fall, etc. etc.
Other times, if you crafted them to a point, and death isn't a natural resolution to the character's story... where do they go? I'm pretty sure that question is why Star Wars EU existed after Episode VI. Here are all these characters, they just went on an epic journey... now what? I think somewhere out there, someone will always ask: now what?
For us as creators, if we want to answer the "now what?" scenario, sometimes it's best to step back, work on other things. In the end I think each individual character determines what path they inevitably are set down. As much as we may try to fit Han Solo in to life as a General, he'll always be a smuggler at heart, sort of thing.