Get yourself a cheapo multitester from Maplin or somewhere, less than a fiver,set it to the 'amps' range, and connect it to the positive side of the battery between the battery terminal and the positive lead.
If it shows a discharge with everything turned off then all you need to do is start pulling fuses one by one until the discharge stops-then you've found the faulty circuit.is this what the mechanic did? thats how you track this sort of fault down!!
Obviously some things run all the time like radio setting saver circuit and the clock and immobiliser circuits, but what you're looking for is a change from an unexpected circuit, such as a window motor circuit or similar....
But it could of course just be a faulty battery even if it is new, but then i assume your mechanic would have put the drop tester on it to check!!