There are two well known scholarly points of view concerning this issue.
1- That it begins from the time a person breaks his wudoo’ after putting them on
2- That it begins from the time he first wipes over them after breaking his wudoo’.
The first view was held by Abu Haneefah, al-Shaafa’i and Ahmad and their companions, but we do not know of any evidence worth mentioning that they had for that, apart from their own opinions. Hence some of their companions differed from them as we shall see below. I do not know of any precedent for them among the Sahaabah, unlike the second view, for which there is the saheeh ahaadeeth and the fatwa of ‘Umar ibn al-Khattaab (may Allaah be pleased with him).
As for the Sunnah, there are the saheeh ahaadeeth which were narrated from a number of the Sahaabah in Saheeh Muslim, the four Sunans, the Musnads and elsewhere, among which is the report that the Prophet (peace and blessings of Allaah be upon him) enjoined wiping (over the socks or khufoof). In some reports it says that he granted a concession allowing wiping (over the socks or khufoof). In others it says that he made (the time period) for wiping for the non-traveller one day and one night, and for the traveller three days and three nights. It is very clear that the hadeeth is referring to the start of the period for wiping over the khufoof or socks, which begins when one wipes over them (for the first time?), and that is a refutation of the first views, because what it implies, as they stated in al-Furoo’ is that the one who prays Fajr just before the sun rises, then breaks his wudoo’ at dawn on the next day then does wudoo’ and wipes over his socks or khufoof for the first time to pray Fajr, may not do so after that, so can it be said of a person in such a case that he has wiped over them for one night and one day? But according to the second view, which is more correct, he may wipe over them until just before dawn on the third day. Indeed, they said something stranger than what we have mentioned, which is that if he breaks his wudoo’ and does not wipe (over his sock etc.) until one day and one night have passed, or three days if he is a traveller, then the time for wiping has ended and it is not permissible to wipe over the khufoof or socks after that, until he puts them on again after doing wudoo’.
So they deprived him of benefitting from this concession, based on this opinion that is contrary to the Sunnah. Hence Imam al-Nawawi did not could not but adopt a view contrary to that of his madhhab because of the strength of the evidence. After mentioning the first opinion and those who followed it, he said (1/487):
Al-Awzaa’i and Abu Thawr said: The period begins from when he first wipes over them after breaking his wudoo’. This was narrated from Ahmad and Dawood, and it is the more correct view based on the evidence. It was also favoured by Ibn al-Mundhir, and a similar view was narrated from ‘Umar ibn al-Khattaab (may Allaah be pleased with him). Al-Mawardi and al-Shaashi narrated from al-Hasan al-Basri that it begins from the time one puts on (the socks or khufoof), and those who say it starts from when one wipes for the first time quoted as evidence the words of the Prophet (peace and blessings of Allaah be upon him), “The traveller may wipe [over the khufoof or socks] for three days.”
These are saheeh ahaadeeth, as stated above. This clearly states that one may wipe over them for three days, and that can only apply if the period starts from the first time one wipes over them, because al-Shaafa’i (may Allaah be pleased with him) said: If a person breaks his wudoo’ when not travelling and wipes over [the socks or khufoof] when travelling, then he may complete the period that is allowed for the traveller. So he connected the ruling to wiping (i.e., the first time it is done). Our companions quoted as evidence the report narrated by al-Haafiz al-Qaasim ibn Zakariya al-Matrazi concerning a hadeeth narrated by Safwaan: “from one breaking of one’s wudoo’ to another”, which is a strange addition that is not proven, and by analogy…
I [al-Albaani] say: The analogy referred to, even if it was a sound analogy in and of itself, the condition for accepting it and using it as evidence is that it should not contradict the Sunnah. But because it does contradict the Sunnah, as you can see, then it is not permissible to pay any attention to it. Hence it was said: When there is a report, there is no room for personal opinion. So how about if it is also contrary to the words of the Rightly-Guided Caliph ‘Umar ibn al-Khattaab? I know that some of those who follow unthinkingly ignore the Sunnah when it differs from a report narrated from ‘Umar (may Allaah be pleased with him), as they did with regard to the threefold divorce, so how can they not follow his opinion when it is in accordance with the Sunnah? ‘Abd al-Razzaaq narrated in al-Musannaf (1/209, 807) that Abu ‘Uthmaan al-Nahdi said: I saw Sa’d and Ibn ‘Amr refer a dispute to ‘Umar about wiping over the khuffayn. ‘Umar said: He may wipe over them from the time he (first) wipes over them for a day and a night.
I say: Its isnaad is saheeh according to the conditions of the two Shaykhs, and it clearly shows that (the period for) wiping over the khuffayn starts when from the first time one wipes over them until the same time the next day or night. This is the apparent meaning of all the reports which have been narrated from the Sahaabah concerning the period for wiping over the khuffayn, as far as we know, which was narrated by ‘Abd al-Razzaaq and Ibn Abi Shaybah in al-Musannaf. For example, I may quote what was narrated by Ibn Abi Shaybah (1/180) from ‘Amr ibn al-Haarith who said:
I went out with ‘Abd-Allaah to al-Madaa’in and he wiped over his khuffayn for three days and did not take them off. Its isnaad is saheeh according to the conditions of the two Shaykhs.
The reports from the salaf are in accordance with the Sunnah of the Prophet (peace and blessings of Allaah be upon him) as we have mentioned, so adhere to them and you will be guided by Allaah’s leave.
Risaalah Tamaam al-Nash fi Ahkaam al-Mash by Shaykh al-Albaani (may Allaah have mercy on him), p. 89, 92
And Allaah knows best.