But if they turn away - then We have not sent you, [O Muḥammad], over them as a guardian; upon you is only [the duty of] notification. And indeed, when We let man taste mercy from Us, he rejoices in it; but if evil afflicts him for what his hands have put forth, then indeed, man is ungrateful.
(Answer the Call of your Lord before there comes from Allah a Day which cannot be averted.) means, once He issues the command, it will come to pass within the blinking of an eye, and no one will be able to avert it or prevent it.
(You will have no refuge on that Day nor there will be for you any denying.) means, you will have no stronghold in which to take refuge, no place in which to hide from Allah, for He will encompass you with His knowledge and power, and you will have no refuge from Him except with Him.
The earlier three of the above verses state the end of those people who, as against the virtuous Muslims, remained desirous of the delights and luxuries of this world, instead of caring about the Hereafter. Then in verse 47, they have been advised to repent and embrace faith before the scourge of Doomsday comes upon them. Thereafter, in verse 48, the Holy Prophet ﷺ has been comforted and assured that if these people do not come to their senses, despite your preaching again and again, and despite your tireless efforts, then you should not worry: فَإِنْ أَعْرَضُوا فَمَا أَرْسَلْنَاكَ عَلَيْهِمْ حَفِيظًا "So, if they turn away, then We did not send you as a supervisor over them. You are not responsible but for conveying the message" - 48.
The real test of man in the present world is his ability, irrespective of the circumstances, to give a proper and correct reaction. But man does not do so. When he meets with success, he turns into a vain braggart and when he gets into trouble, he can do nothing but express negative feelings. Such people, who are unable to respond properly to the call for Truth, are by temperament unrealistic. The correct response to the call for Truth is that man should immediately admit to its being such. But he makes it a prestige issue. He thinks that by accepting the call, he will be lowering himself before the person who gives the call. This feeling comes in the way of his acceptance of the Truth. In spite of being convinced of its veracity, he ignores the call on account of personal considerations.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.