The twelfth 節気 “sekki” division of the traditional Japanese calendar is:
大暑
(たいしょ)
“taisho”
‘blistering heat’ // ‘major heat’ (solar term)
The last “kō” microseason within this division is:
大雨時行
(たいう ときどき ふる)
“taiu tokidoki furu”
Great rains sometimes fall
That makes 大雨時行 the thirty-sixth microseason of the year!
It typically lasts 3~7 August.
I couldn’t find たいう as a reading for 大雨 but I suspect it can still be valid in this type of older context. What I found instead was:
大雨
(おおあめ)
“ōame”
heavy rain
However, why wasn’t the repeater のま character (々) used in 時?
時々
(ときどき)
“toki doki”
sometimes
“Tokidoki” is one of my favourite Japanese words and the repeater character is one of my favourite quirks of the Japanese language!
Again, I am sure there is a good explanation and it is just that this is an “old style” of writing…
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Image credit: Tokido is one of my favourite fighting game players! He actually chose his name from the word 時々! He is competing at Evo this weekend!
Annotranslate 
As for “たいう ときどき ふる” (and the other names of these seasons), I think it is more of an interpretive (maybe ‘artistic’) as opposed to a literal reading. For example, the last character 行 generally isn’t associated with “falling (rain)” in Japanese, but maybe it does in Chinese.
As for the lack of the 々 character, I think it’s because that character is usually used with kanji, and in this case we are talking about hiragana. In the actual “大雨時行”, the character 時 is not usually read ときどき anyway, it is とき or じ, or something similar.
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Ah! Thank you! 🙂
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I am tempted to translate/transculturate this microseason into: ‘The Dog Days are breaking, then, thank God!’
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