I know this is an old post to dredge up, but a) this is the first result on Google if you're having this exact issue and use any reasonable search terms, and b) these cases are steeply discounted right now in various places since they are making way for the next gen. So figured I'd leave my 2 cents on a fix for the next person who has this issue.
I had this exact same issue *except* I did not have all the fans turn off when I touched it. In my case, the two side fans would speed up then stop (LED turned off for a second), then speed up again ... over and over ... if I put the fan slider they were connected to in anything other than the lowest position. The other two included fans did not do this, they were fine. I contacted NZXT and they send me a brand new fan controller (it's easy to replace, I love this case). So FYI, yes, they will send you a new fan controller for free with no hassle, if you describe your problem well. It takes a few weeks to arrive.
I installed it and ... same problem. So I started experimenting. It turns out that the issue is that the side fans are, by design / out of the box, attached to a splitter and connected to one fan control slider. If you remove one from the splitter and attach it to one of the other fan sliders, everything starts working perfectly. Must be a design flaw in the fan controller where it's drawing too much power or something.
So, this is not a big deal unless you really wanted to have 6 fans (5 fan controls, one of them hooked up to the 2 side fans), ie. were planning on adding 3 more to the ones it comes with. AND you still have your motherboard's fan connectors available if you need to expand. I'd still recommend the case if it's on sale, this was my most enjoyable build ever, everything was nicely pre-routed, it's sturdy, easy to work in, etc etc. Even with the 2 side fans on low and the two other included fans on high, my temperatures were totally normal / fine. Now that I powered each side fan individually (and while I was at it, threw in a front fan I had laying around), temps are even lower. I have every fan on high except the front fan (which was older and louder), and it works just fine and is quiet. No more fans stopping and starting / speeding up and stopping and speeding up again.