"Don't live to 101, I don't advise it..."

Edith* has silky white hair and bright, gray-green eyes. Her voice is low and raspy and posh, and larger than you would expect from such a tiny lady. She is very deaf, and on close questioning, is not entirely lucid. But she puts up an expert front - "..and are you one of the doctors? Did you have to train for many years?" "..I'm a hundred and 2 months. Don't live to 101...." she smiles wryly. She came into hospital as her GP thought she wasn't quite herself and looked pale. Her haemoglobin was 4.9 (normal >11) though there was no history of bleeding. We gave her a blood transfusion and some iron tablets. She looks a bit pinker now, but where do we go from here? How far do you go looking for a cause of anaemia in someone who is 101?