While we await your answer regarding the integrity of the backup disk, if you have a backup disk that abruptly stops working and no longer appears in AirPort Utility, it usually means the backup disk has suffered some degree of corruption and cannot be mounted. The Extreme gives up attempting to mount it, and it just disappears. When that happens, AirPort Utility will no longer indicate the disk is connected.
In some cases the Extreme will determine the disk needs attention and its LED will flash amber, or (again in some cases) the Extreme itself will no longer appear in AirPort Utility. Depending on your network configuration and complexity, it can even bring down your entire network.
The reason for all those various symptoms is due to the variety of hard disk drive failure modes that can manifest, and the configuration of your network.
In any case, connect the hard disk drive directly to your Mac and use Disk Utility. Then, we get into the "in some cases" again. If the disk is very corrupted sometimes Disk Utility itself will become unresponsive and has to be force-quit. If DU successfully mounts the disk, it may indicate the disk needs "repair" which may or may not be successful. If things get this far it usually isn't, and the "repair" fails.
However, in many cases you can use Disk Utility to erase the hard disk drive, after which you can reconnect it to the Extreme, re-select it in Time Machine's Preferences, and start a brand new set of backups. The disk may continue to work, sometimes for a very long time (years). Eventually though, the unavoidable effects of normal aging will become evident, and the disk will disappear again. Or, Time Machine detects corruption and offers to create a new backup. Or, Time Machine just says it cannot back up. Repeat the cycle.
When that cycle of failures becomes annoyingly frequent, discard the disk. That's one of many reasons one and only one backup disk does not comprise a robust backup strategy. You can connect more than one hard disk drive to the Extreme's USB port, but that definitely requires a powered hub.