In our last attempt to save her (and earn ourselves some green-thumb badges), we gave her a pot transplant (more space for her wiggly roots to grow), fed her some medication (fertiliser tablets), and put her on life support (chopsticks!).
We hope this does her good. Her leaves are still kinda droopy but we are hoping for the best. Lights is very worried about her. For some strange reason, Basil and her seem to have founded a strange kind of feline-plantae bond.
I guess too, we have finally decided, Basil's a she.
One less thing for her troubled mind, now she can solely concentrate on recuperating!