Chris has given some great advice and I agree with it all - there is something I would like to add though.
In my experience Junior BAs usually aren't born - they mutate! The scenario I am thinking of is how I came to be a BA and one I have seen in my capacity as trainer many times: people from IT or the Business get a reputation for problem solving and get dumped in to the role when circumstances in their company change. Sometimes they jump in to the role but most often they seem to be dumped.
The question is - how did they get a reputation for problem solving? Answer: they were working alongside or even in change projects in some capacity and as a problem arose, the analysed it, solved it and got the reputation. So there may be a strategy for you here: instead of lookign for junior BA roles look for roles that involve working alongside projects (e.g. project management office) - in the UK there are always loads of temp agencies trying to fill these positions. Once in a project, make sure you have researched the role of a BA and know the outline of the theory at the very least. Then do your job, watch and wait for your opportunity and start volunteering to help BAs, sort out requirements issues and so on. Get a few months of that under your belt and then you can update your CV to reflect that you have actually been doing analysis, and you might even be able to transfer in the organisation you have been gaining experience in.
You can then start applying for BA roles with the justification of having done the job even though you haven't been called a BA.
Oh - the other things are get testimonials (preferably from Project Managers and BAs) and keep copies of the analytical work you do: suitable anonymised, nothing impresses interviewers like examples of your own analysis and testimonials if you can get get them (I haven't been refused one yet!).
I hope this is useful!
- Guy