This answer was written 3–4 April, 2021. If it’s updated later, I will add notes at the end instead of editing the original answer.
Short Answer: We don’t know.
Longer Answer: We don’t know, but probably.
Venti was the first rate up five star in Genshin Impact, his banner being released right when the game launched, lasting from 28 September 2020 til 18 October 2020. He is also the first five star to have a rerun banner, 17 March 2021 to 3 April 2021.
Although the four stars have changed (First banner was Fischl, Xiangling, and Barbara; second is Sucrose, Razor, and Noelle), because Genshin is quite a new gacha game, there aren’t many patterns the limited banners follow.
Okay, I see three main possibilities for Venti:
- He is not added to the five star pool of Wanderlust Invocation (the standard banner) and remains a limited five star, only available when the Ballad in Goblets banner reruns. This is probably the most likely scenario.
- He is added to the five star pool of the standard banner, Wanderlust Invocation. This is probably the least likely.
- Something else entirely. Like a new banner of previously limited five star characters is made available, Venti’s banner is taken out of rotation, and he is added to the five star pool of this hypothetical new banner.
There used to be a few patterns in limited banners:
- The rate up five star character and any of the rate up four stars do not share an element. This was broken by the Hu Tao banner, with both Hu Tao and Xiangling being of the pyro element. The Venti rerun has Sucrose as a rate up four star, when Venti and Sucrose are both anemo units. The rerun of Childe has Barbara, who is a hydro unit like Childe. Is this a coincidence? A new pattern? Something else? Who knows? (Not us, that’s for sure.)
- Rate up banners last three weeks each and two rate up banners are released each update. This was broken by the Xiao-Keqing-Hu Tao trio during version 1.3. All their banners lasted two weeks each.
- Keqing’s banner is also notable because she is a five star from the Wanderlust Invocation banner (Perma banner) and this was the first time a permanantly available five star character was given a rate up. Possibly, other permanantly available five stars, like Qiqi or Diluc, could get rate up banners in the future.
- Limited banners are all announced during the version trailers. The Hu Tao banner broke this, having Hu Tao as the only character so far who was not announced during the official version livestream. This may have been because she is a funeral perlor director and death during Chinese New Year is not a good sign.
Because of these broken patterns and because Genshin Impact does not have much history available to predict, we can’t do much but guess.
Reruns are new territory for Genshin. There is no official word yet, but I highly doubt that the developers would let Venti sit on the sidelines when he’s a highly desired character and player favorite who can make lots of money.
As for when he would return for a third time, if he ever does: From the limited information available, I would estimate about six months from now.
Venti’s rerun, the first rerun ever in Genshin, is roughly six months from when he was first released last September. Childe’s rerun, the second rerun banner, is also sixish months from his original release date.
Although rerun banners do not go in order — if they did, we would have Klee instead of Childe — a rerun every six months or so seems probable. As developers add more and more rate up five stars, this duration may get longer.
TL; DR — There is no official word on Venti’s availability status once his rerun ends but it seems likely that he will return about six months from now. However, because if the uncertain history of limited banners and the newness of reruns and Genshin in general, that could be really wrong.