When did "妳" become the second person singular feminine pronoun? In Kangxi Zidian, "妳" is listed as an alternate form of "嬭". "嬭", on the other hand, has three meanings: breasts/milk, mother, and feminine given name.

On Zdic.net, there is no classical reference to "妳"'s usage as a personal pronoun.

Considering that the third person feminine singular pronoun "她" is a modern invention by Liu Bannong in 1930s, it is plausible that "妳" only became a pronoun in relatively recent times.

Therefore, when did "妳" become the second person singular feminine pronoun?
Short answer: Before modern times, ‘妳' already existed, but it was pronounced nǎi, and was a somewhat rare variant of 奶, which primarily means milk and by extension breasts, grandmother. Starting in the early 1900s, reformers in China used the same character as a female version of the second person pronoun 你, as it replaces the 人 (person, man) on the left side of 你 with a 女 (woman).

From Wikipedia: 

Following the iconoclastic May Fourth Movement in 1919, and to accommodate the translation of Western literature, written vernacular Chinese developed separate pronouns for gender-differentiated speech, and to address animals, deities, and inanimate objects. In the second person, they are nǐ (祢 "you, a deity"), nǐ (你 "you, a male"), and nǐ (妳 "you, a female")... these distinctions are only made in Taiwanese Mandarin; in simplified Chinese, tā (它) is the only third-person non-human form and nǐ (你) is the only second person form. The third person distinction between "he" (他) and "she" (她) remain in use in all forms of written standard Mandarin.