lala, do you think the job had lots of applicants? You say it is for a really good organisation.
I think you could at least ask the organisation how many applicants they had and (possibly) how many were shortlisted. Just some rough figures. I do think it worth pressing for more feedback. You could ask this as part of a general question on future recruitment - ie is the organisation likely to be taking on more staff soon?
I am applying for jobs in Devon as and when the come up (not many in my field of work). They are public sector jobs, so I have always got feedback of sorts. Sometimes I have to make more than one phone call to get this. I have had some interviews and some knock backs.
One experience with a large Devon organisation left me feeling really gutted! I felt the job had beem made for me - my experience was such a close match to their person specification. They were asking for a very specific set of skills and expereience that I just happened to have. I methodically answered every point on the application form.
But my application fell at the first hurdle - it didn't even get to go to the selection panel. HR told me I was a strong candidate, in their opinion, but they couldn't pass on my application form to be considered for short listing.
The reason? On my four page answer to the person spec, I had missed out a space between two paragraphs (a formatting problem that didn't show up on my own computer) and also, spelt 'Exeter' as 'Exert' due to a too hasty spell check.
So be warned - and it might be worth asking HR if they automatically bin applications with any spelling mistakes.