I had the same problem and had to use Custom pagination in the Load Editor.
I have a suspicion it is not sending the authentication header on the subsequent iterations with the Next URL method.
Use the section "Using Custom pagination with Google Analytics" - my data source (Survey Monkey) has the total number available and a custom page size argument. Set those and divide the total record count by the page size to see how many times you should iterate the loop.
Yours may not be exactly the same, but Custom is pretty flexible
One catch: In order to use the "WITH CONNECTION(querystringvar querystringval)" syntax, you need to define the parameter you want to use in the Connection