Make a "print" layout that has your portal expanded to 10, 30, 300 rows...whatever it takes. Don't use this expanded layout for working, just for printing. That way you can see all of your lines on paper.
Make sure your sliding/printing also says to reduce the enclosing body part so your footer stuff doesn't end up below 14 blank pages...
Another option, is to make a report based on your LineItems table (The one your portal is based on). You can place related fields from your Invoices table in a Header or sub-summary part. Make this a list report and use a Find request to find all records for a given invoice and you can print out an invoice of any length you need.