Praise be to Allah.
The correct view is that there is a set time for reciting the morning and evening dhikrs, because of the time mentioned in many ahaadeeth of the Prophet (peace and blessings of Allah be upon him) in which he said: “Whoever says such and such in the morning…” and “whoever says such and such in the evening…”
But the scholars differed to the exact start and end of the time in the morning and the evening. Some of the scholars said that the time in the morning begins when the dawn comes, and ends when the sun rises. Others said that it ends when the forenoon (al-duha) ends, but the preferred time for dhikr is from when dawn begins until the sun has risen. With regard to the evening, some scholars said that the time (for dhikr) begins at the time of ‘Asr and ends when the sun sets, and others said that the time lasts until one-third of the night has passed. And some of them said that the time for the evening dhikr starts after sunset.
Perhaps the most appropriate view is that a person should strive to recite the morning dhikrs between dawn and sunrise, then if he misses that it will be acceptable if he recites them before the time of the forenoon (al-duha) ends, which is shortly before the time for Zuhr prayer. And he should recite the evening dhikrs between the time of ‘Asr and Maghrib, then if he misses that it will be acceptable if he recites them before one-third of the night has passed. The evidence for this preference is the fact that the Qur’aan urges us to remember Allah in the early morning (bukoor) and in the late afternoon (‘ashiy), which is the time between ‘Asr and Maghrib.
Ibn al-Qayyim (may Allah have mercy on him) said: “Allah says (interpretation of the meaning):
‘and glorify the Praises of your Lord, before the rising of the sun and before (its) setting’ [Qaaf 50:39]
This is the interpretation of what is mentioned in the ahaadeeth, ‘Whoever says such and such in the morning… and in the evening’. What is meant by this is before the sun rises, and before it sets. The time for that is between dawn and sunrise, and between ‘Asr and Maghrib. And Allah says:
‘and glorify the praises of your Lord in the ‘Ashi (i.e. the time period after the midnoon till sunset) and in the Ibkaar (i.e. the time period from early morning or sunrise till before midnoon)’ [Ghaafir 40:55]
Ibkaar means the first part of the day, and ‘ashiy means the latter part. So the time for these dhikrs is after Fajr and after ‘Asr.”
(Summarized from al-Waabil al-Sayyib, 200. See also Sharh al-Adhkaar al-Nawawiyyah by Ibn ‘Allaaj, 3/74, 75, 100).
There are also dhikrs to be recited during the night, as was narrated in the hadeeth: “Whoever recites the last two verses of Soorat al-Baqarah at night, that will be sufficient for him.” (al-Bukhaari, 4008; Muslim, 807). And it is known that the night starts at sunset (Maghrib) and ends at dawn. So the Muslim must strive to recite every dhikr that is connected to a specific time at the right time, but if he misses it, should he make it up or not?
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: “With regard to making it up if he forgets it, I hope that he will be rewarded for that.”