If I were you I'd feed him and leave him alone... dont poke him dont flush him let him die in peace... if there is not any evidence of disease like ick for example (white spots on his fins) there's really nothing you can do... You tried your best now it's up to him to do his part. I don't think your sister should get anymore fish by the way....
leave the tank to let him feel comfortable..If we have a fish thats dying and we can't help like theres no meds to fix them we put a towel over the tank to give it peace and not have the stress of everything else... some live some die... I hope this helped a little its just hard when I can't see whats actually wrong with it... Godd luck anyways