There are many reasons why your cars might stall in the mornings...
Here are just a few... I'm not saying I know everything.. but this might just help you figure out what it is...
-Most new BMWs have more than one fuel check valve and more than one filter that also have check valves in them..( check valve- allows any fluid to only travel in one direction) If any one of your check valves fail and allow fluid to drain backwards or in any directions but towards the motor. Then it might take a try or two to start her up.
--Depends on which make and year.. but if you just turn your key to ON then it will turn your fuel pump on.. thus pushing fuel towards your engine... and then you might be able to start it with no problem.
-- I would dought with less than 50k on these cars that a fuel blockage in the pump line would be at fault.
--You might also want to take a look at any of your intake valves anything that moves or adjustes durring Idel or at start up... sometimes even if your air filter is working you can get dust and grim and it wont allow the valve to move properly putting more stess on selenoid that operates that valve. If its sticking.. then it wont let the engine get air.. and then it will stall.. but that might only happen every now and then.. not every time.
-- The only thing else I can think of happend to my own 97M3... If you have any type small or large.... even minute vacume leak in the vacume system then your computer system is of course going to be able to tell... for example.. I have a crack inbetween my Mass AF sensor and my throttle body... and it would cause my car to start and idel at a higher than normal RPM... and then it would slowly just die... untill right before you think it might just turn off.. the computer system would open my throttle body and give it a ton of air pushing the RPMs back up.. and sometimes even.. it would fail.. and the engine would stop.
The main reason that I wrote all of this is because some of the things that might cause your problem.. are not picked up by the DME unit... ex. fuel check valve... from what I know.. the only want to check those.. is if you get a low fuel pressure indication only right after ignition has taken place... and the only way you would find that out would be to know what your looking for if you started the car with a diagnotic computer hooked up.
I hope this might help.... good luck in finding what your problem is....