It is a real traditional Japanese proverb, 七転び八起き (nana korobi ya oki), literally “seven falls, eight risings.” Japanese dictionaries define it as not being discouraged by repeated failure and rising again each time — and, by extension, as a figure for the ups and downs of life. It has no single author.
What it means
However many times you are knocked down, get up once more. The proverb also describes life itself as a run of falls and recoveries, so it can console as well as urge you on.
Where it comes from
Shogakukan’s Digital Daijisen dictionary explains the phrase as coming from falling down seven times and getting up eight, meaning refusing to be defeated by many failures and recovering each time; by extension it describes how full of rises and falls human life is. Wiktionary gives the same two senses: not giving up until you succeed, and the ups and downs of life.
The arithmetic puzzles many English readers: seven falls should need only seven risings. The proverb dictionary on Kotobank addresses this directly, noting that using eight, one more than seven, puts a determined will never to give up in the foreground, and that eight is traditionally a lucky, expanding number in Japan. It cites the saying in use in Okamoto Kidō’s play Heike-gani (1912) and in a 1952 book on retailing by Sōma Aizō; these are examples of use, not the origin, which is traditional and anonymous.