Praise be to Allah.
The Muslim should be keen to complete his Hajj in accordance with the Sunnah, especially if it is the obligatory Hajj, for an accepted Hajj brings no less a reward than Paradise, as the Prophet (blessings and peace of Allah be upon him) told us. So the Muslim should strive to complete the Hajj in accordance with the Sunnah, and part of the Sunnah is to complete the rituals in the correct order, without interruption, except in cases of necessity.
The best time for doing tawaaf al-ifaadah and sa‘i in Hajj is the Day of Sacrifice, following the example of the Prophet (blessings and peace of Allah be upon him) because he did tawaaf and sa‘i on the Day of Sacrifice, and he said: “Learn your rituals (of Hajj) from me.” Narrated by Muslim (1297).
With regard to the end of the time (for tawaaf al-ifaadah and sa‘i), Ibn Qudaamah (may Allah have mercy on him) said:
The correct view is that the end of the time is not specified, so whenever one does them, it is valid, and there is no difference of scholarly opinion concerning that. Rather the difference of opinion is as to whether a compensatory sacrifice is required. End quote.
In al-Mawsoo‘ah al-Fiqhiyyah it says:
There is no specified end to the time for doing this obligatory part of the Hajj (tawaaf al-ifaadah and sa‘i); rather it may be done on any of the subsequent days or nights, according to scholarly consensus. But Imam Abu Haneefah regarded it as obligatory to do it on the Day of Sacrifice; however if someone delays it until he does it after that time, it is still valid, but he must offer a sacrifice to make up for delaying it. The well-known view according to the Maalikis is that nothing is required if it is delayed, unless it is delayed until the month of Dhu’l-Hijjah has ended; if the month ends, then a compensatory sacrifice must be offered. The two companions of Abu Haneefah [Abu Yoosuf and Muhammad], and the Shaafa‘is and Hanbalis are of the view that nothing is required, no matter how long the delay is. End quote.
Al-Mawsoo‘ah al-Fiqhiyyah (17/52). See also: Adwaa’ al-Bayaan by ash-Shinqeeti (4/406); Fataawa al-Lajnah ad-Daa’imah (11/227).
Shaykh Ibn ‘Uthaymeen was asked about a man who travelled to his country and did not do tawaaf al-ifaadah.
This man must refrain from intimacy with his wife, because he has only completed the first stage of exiting ihram and not the second; if someone has completed the first stage of exiting ihram but not the second, everything becomes permissible to him except intimacy with women. And he must also go to Makkah and do tawaaf al-ifaadah in order to complete his Hajj. End quote.
Fataawa Noor ‘ala ad-Darb (223/15-16).
If this man who left Makkah before doing the tawaaf and sa‘i of Hajj came back during the days of Hajj or during the month of Du’l-Hijjah, and did tawaaf and sa‘i, then his Hajj is valid and he does not have to do anything else.
But if he delayed that until the month of Dhu’l-Hijjah had ended, and he came back and did those actions, then he has done what was required of him and his Hajj is valid, but in order to be on the safe side he should offer a sacrifice to compensate for this delay, as we mentioned above that this is the view of the Maalikis and others, and because some of the scholars think that the time for doing tawaaf and sa‘i, and all the other actions of Hajj, ends when the month of Dhu’l-Hijjah ends, because Allah, may He be exalted, says (interpretation of the meaning): “Hajj is [during] well-known months” [al-Baqarah 2:197].
See: Majmoo‘ Fataawa wa Rasaa’il ash-Shaykh Ibn ‘Uthaymeen rahimahu Allah (21/379).
And Allah knows best.