Prescriptively, the only no-no persona who cannot die is a narrator. Who's left to report the drama if the narrator dies? That causes a big willing suspension of disbelief hiccup. Discretionarily, a narrator can die if he or she is somehow around to report events after his or her death or a new narrator takes up the report mid narrative.
Otherwise, readers form a bond with a viewpoint character. If the viewpoint character is a reader surrogate, the persona whom readers build self-identification with, killing him or her off will cause a shock. Bringing on a new reader surrogate later can leave readers without an anchor to bridge the gap. However, if the narrator is a reader surrogate, there shouldn't be a gap.
A reader surrogate dying a self-sacrificing noble death is a hallmark of a beautifully tragic ending. One dying in the middle of the action, though, I don't know, does it further the plot? In other words, does it build upon the main dramatic complication?
Say the viewpoint character dies without finalizing the main dramatic complication. Then a more heroic, capable viewpoint character takes up the mission. That should work fine.
It's finalizing the main dramatic complication that matters, not who finalizes it, per se. One thing, multiple viewpoint characters trading off a mission mid mission challenges readers, therefore, best for new or early adult reader reading skills and above, who can more comfortably process multiple viewpoints.
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