My own opinion is that it would be cleaner to have one authorization for each loan in which you will be accessing a new credit report.
You could have them reaffirm by initialling and dating the authorization on the current FS, without indicating that the rest of the FS is correct as of the new date.
Otherwise, the risk is that you access the credit file and are later told no such request was made.
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Andy Zavoina
Opinions stated are not necessarily that of my employer.