@nomadandinlove Indeed, there’s currently no option to prevent this from happening unless you do some custom coding or even more code from Asset CleanUp.
However, I remember there were similar requests in the past (stopping cache clearing of other plugins) and I’ve decided to provide an update for this.
If you download the development version (replace the one you currently use) – you have details about how to do this here: https://www.assetcleanup.com/docs/how-to-get-the-development-version-of-asset-cleanup/ – you can use an option to instruct Asset CleanUp to prevent cache clearing for “Cache Enabler” plugin. You can even read about it here: https://www.assetcleanup.com/docs/?p=1502#wpacu-cache-enabler
This change will be eventually pushed in the next official release of the plugin. However, if you need it sooner (as you requested it recently), you can use it and then when you update the plugin (whenever the new version will be released), you will still have it there and working as it should.
I hope it helps! Let me know if you have any questions about it!