Typically they either lack one of the two genes that trigger death, or it has been rendered useless by mutation.
Many norns, especially from the first three breeds, do not have the gene that kills them at extreme age (when ageing drops to zero). The other death gene usually causes death at zero glycogen. This is the one that needs to be missing or mutated to cause an undead norn. This gene is not set to be mutatable in the standard genome, but it is possible with genetic modification.
Note that undead norns can still raise their health to normal levels and continue to live regular lives.