Disappearing cat - where does he go?

Babbage, my chocolate Burmese cat, goes out most mornings and comes back
in the evening. A couple of times now, he has disappeared for a whole
week - he returned yesterday morning from his latest 'holiday'. Someone
has obviously been looking after him and keeping him indoors, as his
claws are very neat, unlike their usual tatty state, and he has
obviously been fed, although he has lost some weight.

When this has happened he comes back in a somewhat neurotic state - he
keeps crying and demanding attention - but settles down in a couple of
days. Whoever has been looking after him has presumably gets fed up with
his behaviour.

Like all Burmese, he is very friendly, and loves people making a fuss of
him, even strangers. I think he often goes into peoples' houses and gets
fed, as he's not usually very hungry when he comes in. One of my
neighbors said he visited her once and ate the chicken she was
preaparing for her lunch. Previous Burmese I've owned have also visited
the neighbors. One used to spend the day with an elderly lady in a house
near me whilst I was at work (he'd scratch on her back door to be let
in), and would be waiting for me at the end of the road when I got back
in the evening.

Has anyone got any ideas for finding out who has been keeping Babbage
when he disappears? I can't really go from door to door asking
questions, as he often follows me for about 1/4 mile up the road when I
go out (he gives up after that), and I suppose it could be anyone in the
street I live in. I think it is most likely to be someone close, though.
I could put a tracking device on a collar, I suppose, I have the
technology. 8-) Another option would be to put a note in all the
letter-boxes.

BTW, he doesn't have a collar - I don't like them as they can cause
quite serious injuries.

Leon