All the customer credit settings are in the Customer record under the Terms settings. The customer will be put on hold for overdue invoices. You could change this customer to be placed on Credit Warning (rather than Credit Hold). If a customer is on Credit Warning you can still enter a Sales Order for them, but only if you have a Credit Override privilege.
I believe you can also amend the hold behaviour by altering the Late Grace Days setting which will give this customer longer to pay an invoice before putting them on hold.