The reason yours won't work might be the same reason CCleaner v2.x won't run as a task run by Acronis True Image as I detailed here v2.x no longer works when launched by Acronis True Image. I had lots of views but no replies.
I was aware that some programs won't run as a scheduled task without a password, which means that your Windows account has to have a password as well. Acronis True Image isn't using the scheduler though, and doesn't include a place to enter a password for the external command you can have it run.
At least in your case, they could have conceivably made CCleaner v2.x conform to how it's supposed to act, which as a scheduled task means it requires a password. If that's the case and they did that on purpose, it's unlikely they'll revert back to their old method, even though it worked better for you and I.
You can test it easily with a password; if you do let us know here. Next you'll probably tell me that you were already running the scheduled task with a password or have already tried it.
Andavari, can you confirm or find out for us if they made such a change in v2.x?
FYI, I just tested Acronis True Image with the new version as of today, v2.02.525, with the same result.