Hi Danny,
If you know that records you expected to see on your report are not selected, the usual culprit is the selection formula or range.
What I would suggest is to temporarily remove the entire selection formula and print, to verify that the records you want do appear (ie partially paid invoices). Also insert into your report the fields you intend to base the record selection upon. This is a check so that when you enter your record selection formula, you can determine which records will and won't be selected.
The current amount field is probably what you want, but the selection formula may need to be based upon this field being greater than zero, rather than a status field. The testing above should point out to you which fields would work.