A little more info is needed here. Does it shut off completely or does the throttle cut off. Does it start back up again after you pull to the side? Do any of the warning lights come on when it does this? Is the SES light on afterwards?
Mine FX35 (2009 facelift) has the same issue. From stationary pulling up the engine gives a hick up and sometime stops. Also when you go reverse the same often happens. The milage is approximately 100km, it is a 3.5 V6 280 hp. Gearbox is replaced after the issue showed up. No effect. Also the engine is cleaned.
Anyone an idea what the issue can be?