Obito as Tony explains Nagato betrayed him and used up his one shot at Rinne rebirth to review people of hidden leaf village (I am assuming using his Rinnegan eyes).
How can Obito perform Rinne rebirth if he got Nagato's eyes that he stole from his corpse after battling Konan (Aren't those Rinnegan eyes exhausted?)
Actually, Nagato's Rinnegan weren't his to begin with. These eyes were originally Madara Uchiha's (or even more accurately, they were originally Madara's younger brother's eyes, though it was Madara who awakened the Rinnegan). Madara's Rinnegan were transplanted into Nagato when he was very young.
Now, if the Rinnegan have ever been show to be able to be exhausted (perhaps in Boruto), I am not aware of it. In the first place, Madara first obtained the Eternal Mangekyō Sharingan, which negates much of the Mangekyō Sharingan's toll, and is supposedly inexhaustible (hence the name "eternal"). One would assume Rinnegan has a similar lifespan, given it is a derivation. Regarding the Rinnegan, the Fandom wiki also says this:
However, Madara's eyes did not become Rinnegan until decades later, when his natural lifespan was nearing its end; this also restored his right eye's vision, which had been lost from his earlier use of Izanagi.
(Fandom cites Naruto chapter 681, pages 13-14)
So it seems that even an ability that can exhaust the Eternal Mangekyō Sharingan, does not exhaust the Rinnegan. Or at least, Madara got a one time fix when his Sharingan evolved. Though it has also been suggested on the answers for this question that his eye recovering had nothing to do with evolving, and was merely a result of the regenerative effects of Hashirama's cells which he incorporated into his body. Danzo's usage of Izanagi might provide further info for whether this is the case. If it is so, then this paragraph would be discounted as useful, as Nagato did not have Hashirama's cells.
Or perhaps it cannot be discounted, as both Obito and Madara do have these cells, so it might explain why the Rinnegan was not exhausted. As soon as they plugged it in, the cells would do their work and undo much of the damage Nagato did.
Where does this leave us? We know Nagato did not exhaust the Rinnegan, despite extensive use of its powers. His own body, however, did suffer quite greatly. Similarly, Obito did not exhaust the Rinnegan when he used it's powers.
