My 2011 FX has had similar issues. When I slow down and then accelerate normally the car seems almost as if it going to stall, so I push the accelerator down more and then it surges and takes off somewhat suddenly - not smooth acceleration as when the car was new. I have about 33,000 miles on the car and recently replaced the battery, front brake pads and tires, so this is the only thing about the car that I do not like. I am going to call Infiniti service and ask if they can take care of this when I bring it in for an oil change, hopefully this coming week. I have owned one FX45, an EX35 an about 3 FX35s and never had anything like this. My first was a 2003 FX45 and I would like to upgrade to a new one, but am waiting for a revamp soon, as the new ones look about the same as my 2011.
Fritz