Trietwentie,
Having recently been through the process and just come out of the pool - I had a similar experience with it all going a bit quiet after the med questionnaire etc.
I had already told BA when I would be available so made a couple of calls to the HR dept who were v helpful and informative in confirming that everything was ok etc and that yes - I was in the pool. As a result I received an informal email of confirmation.
I got the impression that nothing formal would happen until 3 months before a start date as that is when course allocation/planning is done.
In due course and true to their word - I got the job offer and cse date. Therefore in 'my experience' it seems that once you have confirmed an availability date, they work around you to fit you in where they can so you may well have to assume all is ok and take the plunge with your notice..?
Good Luck
SG