Add detail. Is this latest version of macOS? Latest is buggy. The old general rule of waiting for .2 or .3 has become .4 or .5. Else, we crash into surprise bugs... perhaps like this one.
There is a great abundance of "unexpected ejection" information in countless threads here and elsewhere (including Apples own forums and in Amazon enclosure reviews). It has been a problem with some- but not all- enclosures since Big Sur. I've relentlessly tested this with many enclosures- old and brand new- and arrived at a conclusion that it is bug(s) in macOS. Fans/Defenders usually pop into such threads to blame cable, user, user settings, firmware, enclosure manufacturer, etc while generally ignoring the enclosure worked fine before an upgrade to Big Sur or newer... and even more so those cases where people upgrade, crash into this issue, then downgrade and all is fine again. That seems to shout where the problem lies. But some seem to live to redirect blame from Apple.
Unfortunately, I believe the remedy is only waiting for more macOS updates unless you are willing to play Enclosure roulette in search of one that WILL remain consistently connected. If the latter, use it for Time Machine and occasionally check the existing one as there are macOS updates in hopes they finally get around to debugging port management/power management... even if its been about FIVE years now.
If the problem is this one, CCC or SuperDuper won't necessarily fare any better... as it is probably NOT TM
software but port/power management macOS software. There certainly are fans of CCC and SuperDuper but my bet would be on this problem not being one about TM but about macOS... for which
ANY app running on macOS would still be subject to the same ejections.