The cover should have a spring-loaded ball bearing on the middle edge. Does it depress? The cover is manually closed. Press this area firmly at the top and it should seat closed and make a snap. It automatically opens when the bolt slides back either by discharging the firearm or manual cycling of the bolt.
The dust cover is meant to keep dust/debris out of the rifle when not shooting. While shooting it remains open to allow the ejection of the cartridges.