حَيٌّ لَا يَمُوتُ، قَيُّومٌ لَا يَنَامُ
He is living and He never dies, and He is forever sustaining and He never sleeps.
The daleel for this is:
للَّـهُ لَا إِلَـٰهَ إِلَّا هُوَ الْحَيُّ الْقَيُّومُ ۚ لَا تَأْخُذُهُ سِنَةٌ وَلَا نَوْمٌ ۚ
Allah – there is no deity except Him, the Ever-Living, the Sustainer of [all] existence. Neither drowsiness overtakes Him nor sleep. [Al-Baqara 2:255]
الم ﴿١﴾ اللَّـهُ لَا إِلَـٰهَ إِلَّا هُوَ الْحَيُّ الْقَيُّومُ ﴿٢﴾ نَزَّلَ عَلَيْكَ الْكِتَابَ بِالْحَقِّ مُصَدِّقًا لِّمَا بَيْنَ يَدَيْهِ وَأَنزَلَ التَّوْرَاةَ وَالْإِنجِيلَ ﴿٣﴾
Alif, Lam, Meem. Allah – there is no deity except Him, the Ever-Living, the Sustainer of existence. He has sent down upon you, [O Muhammad], the Book in truth, confirming what was before it. And He revealed the Torah and the Gospel. [Al-i-Imran 3:1-3]
وَعَنَتِ الْوُجُوهُ لِلْحَيِّ الْقَيُّومِ ۖ
And [all] faces will be humbled before the Ever-Living, the Sustainer of existence. [Ta-Ha 20:111]
وَتَوَكَّلْ عَلَى الْحَيِّ الَّذِي لَا يَمُوتُ وَسَبِّحْ بِحَمْدِهِ ۚ
And rely upon the Ever-Living who does not die, and exalt [Allah] with His praise. [Al-Furqan 25:58]
هُوَ الْحَيُّ لَا إِلَـٰهَ إِلَّا هُوَ فَادْعُوهُ مُخْلِصِينَ لَهُ الدِّينَ ۗ الْحَمْدُ لِلَّـهِ رَبِّ الْعَالَمِينَ ﴿٦٥﴾
He is the Ever-Living; there is no deity except Him, so call upon Him, [being] sincere to Him in religion. [All] praise is [due] to Allah, Lord of the worlds. [Ghafir 40:65]
and the prophet [saws] said:
إِنَّ اللَّهَ لَا يَنَامُ وَلَا يَنْبَغِي لَهُ أَنْ يَنَامَ
Allah does not sleep, and it does not behoove Him to sleep [Reported by Muslim and others]
These two names of Allah, Al-Hayy and Al-Qayyuum are mentioned together three times in the Quran, as was quoted above. They are among the greatest names of Allah. Some scholars even say that they are (together) the greatest and most majestic name of Allah. This is because they suggest the lofties and most perfect excellence of Allah.
Al-Qayyuum signifies eternity and everlastingness, which Al-Qadiim does not. Scholars say Al-Qayyuum means ‘qaa’imun bi nafsihii, muqiimun li qayrihii’.
All of the beautiful names of Allah revolve around these two names, and their meanings revert to these two.