In my case, the error message "The operator or administrator has refused the request" meant that a previous instance of the task has still been running and the task was configured to not start a new instance if it's already running (the default configuration), so the Task Scheduler refused to start a new instance when the task was triggered.
You can find that option in a select box on the task's Settings tab, under the caption "If the task is already running, then the following rule applies". The default value is "Do not start a new instance".
But that error message is pretty confusing. From the other answers, you may see that it may mean many completely distinct errors. As is usual in Microsoft's products.
Tip
It's helpful to check the History tab of a task. That's where I have found out what's actually going on. There was an event "Launch request ignored, instance already running".
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