Hi Brandon,
I suspect that this is due to the project sponsor not having contribute or manage access to the task (they probably only have view access). Making someone a project sponsor doesn't automatically given them additional access to a project, it just adds them to the project notifications so that they have oversight of what is happening.
In order to fix this, go to the sharing permissions of your task (or project) and add the project sponsor with either contribute or manage access. They should then gain the ability to change task statuses.
Best Regards,
Rich.