I work mainly in Chrome, only open Firefox a couple of times a month. But every day I get dozens of notification windows telling me that "Firefox has Closed. Do you want to clean?" - Firefox has not been opened. It's a little annoying. Some kind of bug is telling CCleaner that a firefox window has opened and closed.
My first thought is firefox is opening in the background to update
Although there is currently a Firefox update, if it's happening 'dozens of times' every day then I'd suspect something else.
I'd suspect that some other app is opening Firfox in the background to check for something, possibly to check for updates.
eg. Do you have automatic updating turned on for Firefox extensions? (Most wouldn't check unless Firefox is already open, but you never know).
However 'dozens of times' gives me another thought; are you using Thunderbird as an email client?
It could be Thunderbird checking for new emails.
The simple solution to prevent seeing these notifications is to change your Smart Cleaning setting for Firefox to clean without a notification.
Whatever is opening/closing Firefox would still be doing it, and CCleaner would still be cleaning it when it closes, just not nagging you when it does.