Not an AirPort issue, really. It is a High Sierra operating system issue, which has added new security.....and AirPorts and AirPort Disks are disappearing for some users as a result.
Try manually mounting the drive.....
Open any Finder window
Click on the Go menu at the uppermost top of the Mac's screen
Click Connect to Server
Enter afp://AirPortIPAddress
For example, if the IP Address of the AirPort router is 10.0.1.10, enter afp://10.0.1.10
Click Connect, and if all is well, the drive will mount on the desktop
If no luck, Apple switched over to smb for some communications, so try smb://10.0.1.10
If still no luck, best to post over in the High Sierra support forum to see if the gurus over there have some workarounds.