The only time I missed a flight (I would rather sit in the lounge for an hour than have to run to the gate!), I was connecting (return) Athens to Johannesburg via LHR on a Virgin ticket. Except VS did not advise me that the leg on BA would land at LGW, not LHR (the outward leg had been from LHR to ATH). Of course, the connecting limo could not beat the M25 traffic jam, so I made the desk 3 mins after the flight had closed. I had been in constant phone contact with them throughout the journey...

VS shrugged their collective shoulders and re-booked me on the following night's flight but refused to allow me another limo service to take me to my overnight accommodation "as the connection from LGW was my allocation for the trip".