820si problem

my 820si has a problem that is baffling me, on a fully charged battery it will run for about a day or so then suddenly the rev counter stops working and most of the other accessories whilst driving. Once stopped when I try to start the battery is flat. Now after charging battery when I turn on ignition light comes on as normal...car starts...ignition/charge light goes out.......stays out whilst driving as normal...then all of a sudden above problem comes again. I have replaced the battery and also had the alternator tested and told it was ok and the problem was the battery...but 2 new batteries later and the problem is still there. any help would be greatly appreciated