How often is the blessing over thunder and lightning to be recited during a storm?
So long as the clouds [of that storm] have not yet become dispersed [one does not repeat the blessing upon seeing or hearing a second thunder or lightning, as] all [of that storms] thunder and lightning is exempt with the original blessing that was said. [In other words, once a blessing is said over thunder or lightning of a group of storm clouds, the blessing is not to be repeated over a second thunder or lightning of that same continued group of clouds even if many hours pass.] However, if the clouds dispersed [and then a second set of clouds returned] between the two thunders or the two lightnings, then [it is considered a new storm and] one needs to repeat the blessing over the second set of thunder and lightning.
One does not repeat a second blessing upon hearing a second thunder or seeing a second lightning of a storm, unless the sky cleared up in the interim and the storm clouds then returned.
What is defined as the clouds having dispersed?
This means that the entire sky has completely cleared up of any [rain] clouds [even from a distance], allowing the sun, moon or stars to shine, and the storm clouds then returned.
If one traveled to a different area and then returned: Some Poskim rule that if one traveled past the storm where the skies are clear and then returned to the area of the storm, a new blessing may be said.
May a new blessing be said the next day if the storm clouds of the previous day did not disperse?
Some Poskim rule that all the above only applies on the same day, however, the next morning [after awakening from sleep], one is to recite a new blessing upon seeing and hearing thunder and lightning, even if it is the same storm and the clouds from the previous day have not yet dispersed. However, from other Poskim it is implied that there is no difference between that day and the next day, and also the next day a second blessing may not be said if the clouds of the previous day’s storm have not yet dispersed. [Thus, during a storm that lasts a few days without any clearing up of the skies, one would only say a blessing on the first sighting and hearing of thunder and lightning and not anytime thereafter.] Practically, those who repeat the blessing the next day have upon whom to rely.
 Seder 13:16; Luach 12:25; Michaber 227:2; Rosh Brachos 9:13; Rabbeinu Yona Brachos; Rif Brachos 43b; Yerushalmi Brachos 9:2; Ketzos Hashulchan 66:13; Piskeiy Teshuvos 227:7; Halacha Berura [Yosef] 227
Other opinions: Some Poskim rule a new blessing may be recited even if the clouds did not disperse, so long as the thunder and lightning ceased for some time. [Implication of Eshkol, Rokeaich, Miuchtam and Riaz, brought in Halacha Berurah ibid]
 The reason: Although the blessing over other sights is only said once every thirty days, that is referring to a case that one sees the same item, however here regarding thunder and lightning that the second thunder and lightning is considered a different item, a new blessing is to be said when the clouds have dispersed and caused Hesech Hadaas. [Bach 227; Olas Tamid 227:1; Kaf Hachaim 227:14; See Ketzos Hashulchan 66 footnote 23]
 Implication of Talmidei Rabbeinu Yona ibid “Shamayim Zachu Beinav” and Lechem Chamudos ibid that it is coming to exclude if the clouds scattered in different directions and remained covering the sky; Elya Raba 227; M”B 227:8; Kaf Hachaim 227:13; Piskeiy Teshuvos 227:7; See Halacha Berurah ibid that from some of the above sources it is implied that it is not necessary for the sky to be become completely cleared of skies.
 Piskeiy Teshuvos ibid
 Mishneh Halachos 10:46; Halacha Berurah [Yosef] 227:31
 Yerushalmi ibid “that day”, brought in Rif 43b, Rosh 9:13; Mamar Mordechai 227:3; Birchas Habayis 30:5; M”B 227:8 based on Yerushalmi; Kaf Hachaim 227:12; Birech Es Avraham 66:3; Halichos Shlomo 23:25; Tzitz Eliezer 18:78; Az Nidbaru 5:32; Piskeiy Teshuvos ibid; Halacha Berurah ibid
 However, the blessing is not to be repeated at night over the same set of storm clouds, even if it was said in the morning of that day, and he slept in the interim in the afternoon. [Birchas Habayis 30:5; Ketzos Hashulchan 66 footnote 23; Piskeiy Teshuvos ibid; Halqacha Berurah ibid] However some Poskim rule the blessing may be repeated that night if the blessing was said in the morning. [Ashel Avraham Butchach 227]
If one woke up before daybreak: However, if he slept a set sleep at night and woke up before daybreak, then he may say a new blessing over thunder and lightning of the same storm, just as is the law regarding Birchas Hatorah. [Birchas Habayis 30:5; Piskeiy Teshuvos ibid; Halacha Berurah ibid; Ketzos Hashulchan 66 footnote 23 that so is possible understanding of Yerushalmi. However, he also suggests that perhaps according to the Yerushalmi it has nothing to do with sleeping, and rather each day a new blessing is required and hence it may not be repeated until daybreak even if one slept.]
 If one did not sleep the night: Some Poskim rule that if one did not sleep the night he may not repeat the blessing. [Implication of Birchas Habayis ibid; Ashel Avraham Butchach 227; Ketzos Hashulchan 66 footnote 23 that it is possible to understand the Yerushalmi that it is the sleep which makes the Hefsek and hence if one did not sleep the night a blessing may not be repeated; Az Nidbaru 5:32; Beir Sarim 5:45; Piskeiy Teshuvos ibid that if he did not sleep the night then since by Birchas Hatorah it is subject to debate, therefore Safek Brachos Lihakel and a new blessing is not to be recited. So also concludes Halacha Berurah ibid] However, see Ketzos Hashulchan 66 footnote 23 that it is also possible that according to the Yerushalmi, a new blessing must be said each new day, irrelevant if one slept, and it has nothing to do with Birchas Hatorah or Hesech Hadaas. So also concludes Chazon Ovadia Brachos p. 467
 The reason: Seemingly this follows the same ruling as Birchas Hatorah, that the nighttime sleep is considered Hesech Hadaas. [Birchas Habayis ibid; Ketzos Hashulchan 66 footnote 23; Tzitz Eliezer 18:78; Piskeiy Teshuvos 227:7]
 Implication of Setimas Haposkim of Admur ibid; Michaber ibid; Tur 227 who all record the ruling of the Yerushalmi but omit its ruling that the next day a blessing may be recited; brought in Ketzos Hashulchan 66 footnote 23; Gedulas Elisha 227:13