Mine would remain closed for a short time when I first purchased mine as well but quickly stopped. This is normal. The dust cover is supposed to pop open when the bolt cycles on any AR-15.
They're not intended to stay closed. Something about the dust cover causing the action to malfunction due to the low pressures of the .22lr cartridge. That's why they ground the little notch in the receiver where the dust cover lock latches. A replacement dust cover may not help you. My Colt/Umarex dust cover won't remain closed either. The dust cover is there basically for show, like the forward assist button.
Likely poor sales. My Kalashnikov has functioned very well but uses the less than ideal Russian side mount optics system. And the mount isn't even standard sized.
I bought it's big brother, the SIG P226 Classic 22 and after lapping the slide it's been a good shooter. My only real complaint is the mismatched colors between the slide and the frame.