I also think there's something important that the writers or editors can easily forget: If you're going to replace a character, give the original a respectful, dignified send-off.
A heroic death, sacrificing themselves knowingly to save the world or their family or whatever, can work, but usually that pisses off the fans, since they don't like seeing their favorite heroes die, even nobly.
(An exception can occur if the character has been through such bad stories that even the fans would view it less as a tragedy and more an act of mercy, like putting the beloved family pet to sleep when it becomes horribly sick; I'm told that the over two-year long "Trial Of The Flash" storyline that ended Barry Allen's title before the CRISIS ON INFINITE EARTHS was so awful, that many Flash fans believed the book was beyond saving, and why there wasn't too much negative reaction to his death against the Anti-Monitor.)
Better, I feel, to do something that removes their ability, but not their desire, to be a hero; perhaps they must give it up for some altruistic reason or other. That clears the deck for the new character while letting the old one ride off into the sunset to a well-deserved happy ending, which doesn't piss off their fans as much, and leaves the door open for cameos, perhaps an ongoing role as a member of the supporting cast, and the ability to return them to heroism at some point down the line, either replacing their replacement or alongside them.
The worst thing to do is send the old character out in a blaze of suck, like Hal Jordan in "Emerald Twilight." Turning him into a mentally unbalanced mass murderer? Guaranteed way to alienate the vast majority of the fanbase. No wonder they didn't accept Kyle Rayner.
I wonder how far back this goes...do you think fans who read Alan Scott and Jay Garrick back in the 40's got pissed when Hal Jordan and Barry Allen came around?