A class not starting every so often....

[Gring]

Hi,

Every so often our A190 decides not to start. What usually happens is: If we were to go for a drive, say for 15 miles, then turn off the ignition, then 5 mins later restart it, all is fine, but then if we were to turn off the engine again after a short drive 90% of the time the car will not restart. It is as if the battery is completely drained (No lights on dash). If we keep trying for anything up to an hour, eventually it decides to start. It is really strange. The battery is fine, I have checked that, the starter motor seems fine.
Has anybody else experienced anything like this? Or know what it could be?

Thanks in advance