If the Plan Document says something about deferral elections for rehires, then do what it says.
In any case, as hr for me says, check on what, if anything, the payroll processing system does.
Whatever the procedure you end up using, make a note of it so that the Participants and you and your successors know what to expect.
For example, it could be a note on or with the election form that says, "If your employment with our fine company terminates, your deferral election becomes void. If you are later rehired, your deferral election will be the default deferral rate in effect at that time unless you file a different deferral election." or "Your deferral election will change only when you file a new deferral election. Changes in your employment status do not change your deferral election."