Rule runs over and over, infinitely

I have a fairly simple renaming (appending date) rule set up.

Hazel 4.3.4 keeps running the rule over and over, appending date repeatedly, indefinitely. Any tips? The folder is at iCloud-synced Desktop on Mojave.

If the renamed files still matches the rule, then it's possible it will get run again. You should add a condition to the rule to prevent that. Either match the new filename with a pattern or add a tag which you can detect.