Task Scheduler intermittent failure (Error Value: 2147943767)

In Windows 10, I have a Task in the Windows Task Scheduler that triggers at a certain time and also can run on demand. The Task comprises four Actions, each calling the same program with very similar options.

Though the first of the four Actions will occasionally succeed, the Task will always fail on the second action. The failure produces details similar to:

<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
    <System>
        <Provider Name="Microsoft-Windows-TaskScheduler" Guid="{GUID####-##...}" /> 
        <EventID>101</EventID> 
        <Version>0</Version> 
        <Level>2</Level> 
        <Task>101</Task> 
        <Opcode>101</Opcode> 
        <Keywords>0x8000000000000001</Keywords> 
        <TimeCreated SystemTime="1900-01-01T00:00:00.000000000Z" /> 
        <EventRecordID>54906</EventRecordID> 
        <Correlation /> 
        <Execution ProcessID="76" ThreadID="10964" /> 
        <Channel>Microsoft-Windows-TaskScheduler/Operational</Channel> 
        <Computer>ryan-pc.bplogix.com</Computer> 
        <Security UserID="S-###" /> 
    </System>
    <EventData Name="TaskStartFailedEvent">
        <Data Name="TaskName">\Name-of-Task</Data>
        <Data Name="UserContext">DOMAIN\user</Data>
        <Data Name="ResultCode">2147943767</Data>
    </EventData>
</Event>

If the first Action fails, the Task reports:

The operator or administrator has refused the request 0x800710E0

I use the "Run whether user is logged on or not" option, and I see results like these whether or not I have checked the "Do not store password. The task will only have access to local computer resources." option (and again, what does that option mean?). The user has "Log on as a batch job" rights, and I can run the same command in a normal non-elevated command prompt window successfully every time.

What could cause this failure and if it fails sometimes, why would it succeed at all?