All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu`alayhi wa sallam, is His slave and Messenger.
Scholars disagree over the topic of the death of the soul; however, the most authentic opinion on that point is that of Ibn Abi Al-ʿIzz Al-Hanafi who, in Sharh Al-ʿAqeedah At-Tahaawiyah, said, “The authentic opinion is that 'death of souls' means the departure of the bodies and getting out from them. If this is the meaning intended by this concept (i.e., death of the soul), so the meaning will be that it will taste death; however, if the intended meaning is that it would entirely perish, the soul does not die in the very sense of this word; rather it remains alive either in the Paradise or in Fire.”
Anyway, conviction on the eternity of the soul does not render the person an unbeliever, nor does it include any act of drawing a comparison between the Attributes of Allah, the Exalted, and those of His creatures. In fact, conviction – under this case – resembles our conviction in the eternity of Paradise and the Fire, stressing meanwhile that there is a big difference between the Eternity of the Lord of the Worlds and that of the creatures since the first is an Essential Attribute of Allah and one of His, the Exalted, Attributes of All-Perfection. As for the eternity of the creatures, it is kept by the Command of Allah, the Exalted, in accordance with His Will. In other words, the Creator has the Attributes that befit Him, and the creatures have the attributes befitting them. Commenting on Al-ʿAqeedah At-Tahaawiyah, Ibn Abi Al-ʿIzz Al-Hanafi said, “The All-Living (Allah) is the One for Him life is one of His Essential Attributes; He is the One Who grants this eternal life to some creatures, so it remains as long as He wishes, not because eternity is essential for it. All the Attributes of Allah are totally different from those of His creatures; the Creator has the Attributes that befit Him, and the creatures have the attributes befitting them.”
Allah knows best.