The majority of scholars require الوضوء for valid الطواف; the Hanafi school considers it واجب but not a strict condition. If الوضوء breaks mid-الطواف, renew it and resume from where you stopped.
The majority of scholars from the Maliki, Shafi'i, and Hanbali schools hold that ritual purity (tahara) is a condition (shart) for the validity of الطواف, meaning الطواف performed without الوضوء is invalid and must be repeated. Their primary evidence is النبي's statement that الطواف is like الصلاة, and since الصلاة requires الوضوء, so does الطواف. Additionally, النبي (صلى الله عليه وسلم) himself performed الوضوء before his الطواف and instructed Aisha to do the same.
The Hanafi school takes a different position: they consider الوضوء for الطواف to be واجب (واجب) but not a condition for validity. This means that if someone performs الطواف without الوضوء, the الطواف is technically valid but the person has committed a sin and must offer a penalty sacrifice (dam). This distinction can be relevant for الحجاج who find themselves in difficult situations regarding maintaining الوضوء in massive crowds.
If your الوضوء breaks during الطواف, عند the majority position, you should leave the Mataf, perform الوضوء at the nearest facility, and then resume your الطواف from the circuit where your الوضوء broke — you do not need to restart from the beginning. Wudu facilities are available throughout the Haram complex. Given the extreme الحرارة and physical exertion, carrying a small water bottle and making الوضوء before starting الطواف is essential planning.
النبي (صلى الله عليه وسلم) said: 'الطواف around the House is like الصلاة, except that Allah has permitted speaking in it.'
النبي (صلى الله عليه وسلم) said: 'الطواف around the House is like الصلاة, except that Allah has permitted speaking in it.'
Source: ابن قدامة, Al-Mughni; al-Kasani, Badai al-Sanai
النبي (صلى الله عليه وسلم) said: 'الطواف around the House is like الصلاة, except that Allah has permitted speaking in it.'
Sunan al-Tirmidhi #960 (sahih)