Ya know, this is so very similar to problems I had when I first bought my Q. After thinking it over, I think it could very well be your MAF. You don't have the bucking/coughing symptom, but I had that same sudden stalling you describe. It would stall on me when I let off the gas coming down an off-ramp or approaching a stoplight, for instance. I never had any idle hunting, either, like others have described. I replaced the fuel pump and also pulled the FPCU out to take a look inside. I didn't see any burnt spots and it's been working fine ever since. The new fuel pump didn't make any difference. My problem was a dirty (and eventually failed) MAF.
What made me reconsider is your description. When it stalls on you, you haven't been accelerating, ie, kicking your pump into high speed and heating the FPCU circuits. Of course, you should pull the FPCU anyway and take a look at it. Dennis has said that he's seen these intermittant problems with FPCUs long after the pump has been replaced, but I'm thinking you're having MAF troubles. I think PopPop has a couple MAFs for sale in the Infiniti Cars/Parts section. You should consider picking one up and swapping it - extremely easy. Short of that, you can just give the MAF element a cleaning according to instructions on Q45.org:
http://www.q45.org/maf.html
I cleaned mine whenever the symptoms reappeared, but it eventually became marginal and I replaced it with one I got through car-part.com. No trouble since.
They're both easy fixes. Check your FPCU for symptoms of circuit board failure and clean your MAF, then go from there.