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 তাওয়াফ, meaning তাওয়াফ performed without অযু is invalid and must be repeated. Their primary evidence is নবী করীম's statement that তাওয়াফ is like সালাত, and since সালাত requires অযু, so does তাওয়াফ. Additionally, নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) himself performed অযু before his তাওয়াফ and instructed Aisha to do the same.
The Hanafi school takes a different position: they consider অযু for তাওয়াফ to be ওয়াজিব (wajib) but not a condition for validity. This means that if someone performs তাওয়াফ without অযু, the তাওয়াফ is technically valid but the person has committed a sin and must offer a penalty sacrifice (dam). This distinction can be relevant for হাজীগণ who find themselves in difficult situations regarding maintaining অযু in massive crowds.
If your অযু breaks during তাওয়াফ, according to the majority position, you should leave the Mataf, perform অযু at the nearest facility, and then resume your তাওয়াফ from the circuit where your অযু 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 অযু before starting তাওয়াফ is essential planning.