A few things you can check.... make sure you didn't add restrictions to your API token (for example if you are having it only work for certain IPs) or restrictions on date/accounts it can be used on.
I suppose maybe something is wrong with the token itself... you could always create a new one just to be sure.
Yeah, I just moved some sites to a new server and got that "Trying to access array offset on false" error when looking at the Cloudflare settings page in the XF admin area.
These sites were using the old API-created tokens and I suspect they were tied to a specific IP address (I can't tell because I can't see them via the Cloudflare UI given they are API-only).