The śāstras say:

pāpiṣṭhā ye durācārā
 deva-brāhmaṇa-nindakāḥ
apathya-bhojanās teṣām
 akāle maraṇaṁ dhruvam

“For persons who are pāpiṣṭha, very sinful, and durācāra, misbehaved or very unclean in their habits, who are against the existence of God, who disrespect Vaiṣṇavas and brāhmaṇas, and who eat anything and everything, untimely death is sure.” It is said that in Kali-yuga one has a maximum lifetime of one hundred years, but as people become degraded, the duration of their lives decreases (prāyeṇālpāyuṣaḥ). Because Ajāmila was now free from all sinful reactions, his lifetime was extended, even though he was to have died immediately. When the Viṣṇudūtas saw Ajāmila trying to say something to them, they disappeared to give him a chance to glorify the Supreme Lord. Since all his sinful reactions had been vanquished, he was now prepared to glorify the Lord. Indeed, one cannot glorify the Lord unless one is completely free from all sinful activities. This is confirmed by Kṛṣṇa Himself in Bhagavad-gītā (7.28):

yeṣāṁ tv anta-gataṁ pāpaṁ
 janānāṁ puṇya-karmaṇām
te dvandva-moha-nirmuktā
 bhajante māṁ dṛḍha-vratāḥ

“Persons who have acted piously in previous lives and in this life, whose sinful actions are completely eradicated and who are freed from the duality of delusion, engage themselves in My service with determination.” The Viṣṇudūtas made Ajāmila aware of devotional service so that He might immediately become fit to return home, back to Godhead. To increase his eagerness to glorify the Lord, they disappeared so that he would feel separation in their absence. In the mode of separation, glorification of the Lord is very intense.