External USB3 hard drive has suddenly become slow
Addressing your questions in order...
- what may have caused that [backup to take 1:45]?
- is it a signal of imminent failure?
- what tools may I use to investigate the issue?
Cause
Since you didn't get any read/write errors on CCC, it's entirely possible that you didn't have enough USB bandwidth to copy files at the speed it normally does. I've had instances on several Macs, all running different versions of macOS suddenly lose connectivity to USB audio devices, and have slow transfers to USB drives. A simple reboot and the problem goes away. (Normally, I would reset the USB bus, but found it easier to simply perform a system reboot).
Now, for me, this always occurred with bus powered devices. Devices connected to a USB hub with external power supplies or devices that had their own power adapters never exhibited these problems so I chalked it up to too much power draw on the USB bus.
Imminent Failure?
Is this a signal of imminent failure? Not exactly. Read/Write errors are symptomatic of imminent failure. It's entirely possible that the USB controller on the external drive simply "glitched" or pulled to much power thus improperly resetting the USB bus. If the problem exists after a reboot, you should start paying closer attention because it could be the USB port on the Mac mini equally likely as the USB interface of the external drive.
Diagnostic Tools
What tools can you use? Unfortunately, none. Getting disk status is limited to what ATA commands the USB to SATA controller on the enclosure is capable of delivering. The WD Elements Portable is Western Digital's entry level line of external drives so they don't have any software available for diagnosis. However, one step up, the Elements SE line, does have Windows/Mac software specifically for diagnosing those drives. You could give the software a go; the worst that can happen is it doesn't work for your drive.
Going Forward
Your Mac mini is in a remote location that's now almost impossible to access. When selecting your backup hardware, go for more "robust" products like the WD Passport or even the larger "desktop" drives with their own power supply. You also want to have more than one in the event one fails.
If you go this route, don't back up the backup. Let it make it's own backup because if you happen to back up garbage onto the first, you don't want the second to be garbage as well. I would even look to backup to the cloud for good measure.