Both Henshell and Schuessler think that the word that 哀 stands for was originally derived from what was basically a lamenting sound. Something like English Aaah (with descending tone, like in Aaah, how sad, NOT the Aaah that hurts!). 衣 used to have a sound like AI and was therefore the phonetic. 口 is simply the mouth that is making the lamenting sound.¹
So how to connect clothes 衣 to ‘lament’ now the phonetic (I instead of AI) is broken? Wieger (16 C) sees a ‘mourning dress’.
The character 衰, which looks very similar to 哀 now (only 一 added in the modern form) used to be rather different. It’s still visible in seal shape (displayed at the right). It had no kuchi 口, instead inverted plants, indicating the straw that people used to make a raincoat from (which was the word it was used for, hence cloths 衣 as the signific).
This word raincoat is now conveyed by 蓑 (which adds the signific grass to restore the meaning of the obscured plants). In Japanese it is used for a similar word, mino, ‘straw raincoat’ (although I doubt it that either that type of coat or the word mino is still being used). The original 衰 was used to write a completely different word, probably because the scribes needed a character for a word with roughly that sound in Chinese (hence the necessity to add grass to the orignal raincoat character, to keep it apart from that different word).²
This different word means something like ‘decline, falter, decrease, weaken’. There’s no relation with the straw raincoat. Its like writing rain instead of reign (when you don’t know how to spell the latter) in English, it sounds the same, that’s all.
Attempts at mnemonics for all three of them: At one 一 time a straw raincoat 蓑 surely withers away 衰, a rainy day lament 哀 that is. You lament 哀 because you get wet (and weaken 衰) in the rain, with no straw raincoat 蓑 !
1. Henshell 998; Schuessler, p. 149.
2. Henshall 1456; Qiú p. 265: “[衰] depicts grass on clothing and is the protoform of ″蓑″ suō ″grass raincape.″ The use of {衰} shuāi in the sense of ″decline, weak″ is a borrowed usage.”