First place to start when troubleshooting a specific camera being offline or not recording would be to go to the archive server it is supposed to be recording to and try to navigate to the cameras interface (http://camIPaddress/).
After you confirm this is not a network or camera related issue (meaning you can see the camera's live view from the interface), go to the ESM Admin interface and double-check the settings. (If you are not able to get to the camera's interface, this is a camera or network related issue.)
Common issues include incorrect authentication, incorrect camera model selected, no archive server or archive server volume selected, motion detection lines not being present, and the enabled button not checked.
Please note that ESM is on a delayed time to try to reconnect to the camera once it fails repeatedly. You may just need to wait after correcting the issue in the ESM Admin interface for ESM to retry the process to successfully connect again.