Halachipedia, basing its reading on Mishna Brurah, says you can say the b'racha more than once in a day and, technically, even over the same storm if you took your attention away between sightings, though they conclude that it's once per rainbow and it has to clear before you can say a second b'racha:
Mishna Brurah 229:2 writes that even within 30 days one can make the Bracha again upon seeing another rainbow similar to the laws of seeing lightning and hearing thunder where the original sight has ended. [In glosses 'BeYitzchak Yikarei' to MB (loc. cit.) Rav Nebenzahl] writes that the number 30 used by the Mishna Brurah wasn’t specific since it’s possible to make the Bracha more than once in a day. [(]See Vezot HaBracha (pg 156, chapter 17) who quotes Mishna Brurah as saying that one can make another Bracha as long as one removed one’s mind from the rainbow. However, the language of Mishna Brurah implies that the rainbow must clear up before one can make another Bracha.[)]
Others are of the opinion that even without taking focus off the cloud one may make the blessing again as long as the cloud disappeared and then reappeared (KeMareh HaKeshet 12:22).