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 Tawaf, meaning Tawaf performed without wudu is invalid and must be repeated. Their primary evidence is the Prophet's statement that Tawaf is like prayer, and since prayer requires wudu, so does Tawaf. Additionally, the Prophet (peace be upon him) himself performed wudu before his Tawaf and instructed Aisha to do the same.
The Hanafi school takes a different position: they consider wudu for Tawaf to be obligatory (wajib) but not a condition for validity. This means that if someone performs Tawaf without wudu, the Tawaf is technically valid but the person has committed a sin and must offer a penalty sacrifice (dam). This distinction can be relevant for pilgrims who find themselves in difficult situations regarding maintaining wudu in massive crowds.
If your wudu breaks during Tawaf, according to the majority position, you should leave the Mataf, perform wudu at the nearest facility, and then resume your Tawaf from the circuit where your wudu broke — you do not need to restart from the beginning. Wudu facilities are available throughout the Haram complex. Given the extreme heat and physical exertion, carrying a small water bottle and making wudu before starting Tawaf is essential planning.