Resting during sa'i is boleh according to the consensus of scholars from all four schools of jurisprudence. A jamaah haji may sit down at Safa, Marwah, or anywhere along the Mas'a corridor to rest, drink water, or recover from fatigue without invalidating their sa'i. The continuity (muwalah) of sa'i is sunnah (mustahab) but is not a condition (shart) for its validity menurut jumhur ulama.
Sheikh Ibn Uthaymeen explicitly stated that taking breaks during sa'i for rest, water, or to use the restroom is boleh, and the jamaah haji resumes from where they stopped. He noted that the Mas'a is a long corridor (approximately 450 meters each way), and performing seven complete laps is physically demanding, especially in the panas. Islam does not impose unnecessary hardship, and resting is a natural and permitted response to fatigue.
If the iqamah for an wajib shalat is called during sa'i, the jamaah haji should stop, join the congregational shalat, and then resume their sa'i from the point where they stopped. Sheikh Ibn Baz confirmed this ruling, adding that resting on Safa or Marwah to make doa (doa) is actually from the Sunnah, as Nabi used to make lengthy doa-doa while standing on Safa and Marwah. The key point is that the jamaah haji must complete all seven laps — the breaks in between do not invalidate the previously completed laps.