The Prophet ﷺ used to observe retirement (i'tikaf) to the mosque during the last ten days of Ramadan till Allah took him, and then his wives observed retirement to the mosque after his death.  

أَنَّ النَّبِيَّ ﷺ كَانَ يَعْتَكِفُ الْعَشْرَ الأَوَاخِرَ مِنْ رَمَضَانَ حَتَّى قَبَضَهُ اللَّهُ ثُمَّ اعْتَكَفَ أَزْوَاجُهُ مِنْ بَعْدِهِ  

The Prophet ﷺ used to observe i'tikaf during the last ten days of Ramadan. One year he did not observe i'tikaf. When the next year came, he observed i'tikaf for twenty nights (i.e. days).  

أَنَّ النَّبِيَّ ﷺ كَانَ يَعْتَكِفُ الْعَشْرَ الأَوَاخِرَ مِنْ رَمَضَانَ فَلَمْ يَعْتَكِفْ عَامًا فَلَمَّا كَانَ الْعَامُ الْمُقْبِلُ اعْتَكَفَ عِشْرِينَ لَيْلَةً  

When the Messenger of Allah ﷺ intended to observe I'tikaf, he prayed the fajr prayer and then entered his place of seclusion. Once he intended to observe I'tikaf during the last ten days of Ramadan. She said: He ordered to pitch a tent for him, and it was pitched. She said: The other wives of the Prophet ﷺ also ordered to pitch tents for them and they were pitched. When he offered the fajr prayer, he saw the tents, and said: What is this ? Did you intend to do an act of virtue ? She said: He then ordered to demolish his tent, and it was demolished. Then his wives also ordered to demolish their tents and they were demolished. He then postponed I'tikaf till the first ten days, that is of Shawwal. Abu Dawud said: This tradition has been transmitted by Ibn Ishaq and al-Auza'i from Yahya b. Sa'id in a similar manner, and Malik narrated it from Yahya b. Sa'id, saying: He observed I'tikaf during twenty days of Shawwal.  

كَانَ رَسُولُ اللَّهِ ﷺ إِذَا أَرَادَ أَنْ يَعْتَكِفَ صَلَّى الْفَجْرَ ثُمَّ دَخَلَ مُعْتَكَفَهُ قَالَتْ وَإِنَّهُ أَرَادَ مَرَّةً أَنْ يَعْتَكِفَ فِي الْعَشْرِ الأَوَاخِرِ مِنْ رَمَضَانَ قَالَتْ فَأَمَرَ بِبِنَائِهِ فَضُرِبَ فَلَمَّا رَأَيْتُ ذَلِكَ أَمَرْتُ بِبِنَائِي فَضُرِبَ قَالَتْ وَأَمَرَ غَيْرِي مِنْ أَزْوَاجِ النَّبِيِّ ﷺ بِبِنَائِهِ فَضُرِبَ فَلَمَّا صَلَّى الْفَجْرَ نَظَرَ إِلَى الأَبْنِيَةِ فَقَالَ مَا هَذِهِ آلْبِرَّ تُرِدْنَ قَالَتْ فَأَمَرَ بِبِنَائِهِ فَقُوِّضَ وَأَمَرَ أَزْوَاجُهُ بِأَبْنِيَتِهِنَّ فَقُوِّضَتْ ثُمَّ أَخَّرَ الاِعْتِكَافَ إِلَى الْعَشْرِ الأُوَلِ يَعْنِي مِنْ شَوَّالٍ