He had oppertunities on Namek and after the battle with Freeza...and all during the Cell Saga and stuff.
Poor Nappa :(
Because Vegeta never cared about him all that much I guess. Also considering that Vegeta was the one to kill him there is no way Nappa would have stayed loyal. Even if he did, by Namak Nappa would have been a weakling, which Vegeta would have no tolerance for.
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