Well, this is disappointing. I'm having the exact same issue. Stick lights blink, and then it has a new center.
I'm running Windows 7 64-bit, I do NOT use Teamspeak at all, and I have the latest Saitek drivers. Note that just sitting here, NOT in Elite Dangerous, I can see the stick lights blink every 5 minutes or so. The throttle lights don't blink.
I've disconnected and reconnected the "PS/2" cable repeatedly. I've tried 2 different USB ports on my PC (2.0 and 3.0), but I don't think it's that because the throttle never goes out and windows never loses contact with it. I've also tried a powered USB hub (but the driver couldn't see the unit at all, so it didn't work).
I say this is disappointing because I JUST got this thing, it seemed to work great for a couple days, and now has this pretty continual problem. I'd return it, but now I really don't know if I want a replacement since this seems to be a KNOWN problem with these things. If there's a workaround, I'm fine with that, but it seems like it is more of a hardware issue. That's concerning, to say the least.
I'm considering returning it and getting the X52 Pro...but from what I can tell, it suffers from the same kind of problem. Others don't have any issues...so it's just luck of the draw? I hate the lack of available HOTAS' out there...