It says that he failed twice + the last time where he ended up passing after all when he learned the Kage Bunshin.
I read somewhere that we are shown he starts at the same time as the other contemporary genin, and we know he was in the same class as Shikamaru, Choji and Kiba, as they skip class several times, and Sasuke as they start their rivalry early.
I would guess that there are Genin-exams three or four times a year or maybe 3-4 times over a few months, and maybe extraoridinary tests for exemplary students that want to take it (itachi, 4th hokage, kakashi). Then they start their time as Genin at the same time no matter what, so everyone can be assigned to a proper genin-team with the best balance according to strengths and weaknesses. Sasuke being overall exemplary, Sakura super-smart but not very athletic and Naruto being quite athletic but not very school-smart makes for a very balanced team.
As some mentioned, it might change according to peace-time and war-time, or maybe in accordance to how many students there are. When looking at Boruto-classes (yes I read that as well. I have a lot of time.) there one is a repeater as well. 7times I think? and he is clearly older than the others, but probably not more than a year or so since he still seems on the same wavelength as the other kids.