Glad I found this thread - I'd like to share our experience also, as it was very interesting.
My wife and I bought an FNS9 about 3 months ago and have had a few failures to extract on each trip to the range. Sometimes the last round in the mag, sometimes another round gets jammed on the previous un-extracted case. We've probably put about 1000 rounds through the gun, cleaning after almost each trip to the range (after the first time, made sure to get the extractor nice and clean).
In a training class this month at KR Training, a couple of FTEs occurred again, and an instructor tried the gun to see what he thought. Not only did he have a failure to extract, but a few rounds later, he got two shots with a single trigger pull. If it had been me doing it, I would have suspected poor trigger control, but he is very experienced. Also, those two shots were much more rapid than you can get by poor trigger control.
We sent the gun to FNH, explaining both the double-fire and the failure to extract problems. They replaced the fire control assembly and sent it back. We went to the range last weekend, where we had 6 failures to extract (4 for me, two for my wife). We were making an effort to avoid limp-wristing, so I don't think that's it (and, certainly, the KR instructor had a good grip!).
Usually, we use the Winchester White Box ("range pack") 115 grain rounds, though last weekend we used Remington 115 grain rounds ("range bucket"). BTW, we have also been shooting an XD MOD.2 subcompact and an M&P Shield with the same ammo, with zero failures to extract to date.
Need to think now whether to try to have the FNS serviced again, or just give up on FNH. Maybe will try some +P rounds first to see if that makes a difference.