The vet agreed with me that she looked terrible - she's lost a lot of weight and her fur is dull, matted and looks like it's developed a bad case of dandruff, so all in all, it's not good.
The vet gave her a vitamin shot and advised that before we bring out the big guns (haemo and some sort of drug that messes with the brain), I take her to my Mum's and leave her there for a week or two, to see if she comes round where there's no distractions (i.e. Manasse). If she does, then we can be certain that the problem is psychological rather than physical; and then if re-introducing her here causes renewed problems, I'll have to think of another solution -- but which of my cats to give up? I love them both...Let's hope I won't have to make that choice.
I phoned my Mum; luckily, she's willing to have Leila over for a couple of weeks.