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 wudhu is invalid and must be repeated. Their primary evidence is Nabi's statement that Tawaf is like shalat, and since shalat requires wudhu, so does Tawaf. Additionally, Nabi (shallallahu alaihi wa sallam) himself performed wudhu before his Tawaf and instructed Aisha to do the same.
The Hanafi school takes a different position: they consider wudhu for Tawaf to be wajib (wajib) but not a condition for validity. This means that if someone performs Tawaf without wudhu, 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 jamaah haji who find themselves in difficult situations regarding maintaining wudhu in massive crowds.
If your wudhu breaks during Tawaf, according to the majority position, you should leave the Mataf, perform wudhu at the nearest facility, and then resume your Tawaf from the circuit where your wudhu broke — you do not need to restart from the beginning. Wudu facilities are available throughout the Haram complex. Given the extreme panas and physical exertion, carrying a small water bottle and making wudhu before starting Tawaf is essential planning.