First, I'm a little unclear on the procedure you're using. Are you entering the invoices first, using an Invoice Batch, and then creating a manual cheque batch to pay the invoices? Or are you creating a manual check (cheque) batch and entering and paying these as cash invoices?

Do you make a backup before you print the cheques? Does everything pass the data integrity check?

The invoices selected to pay in the Adagio Payables system check run (accessed from the print/post checks menu as you indicated) are based on the filters specified on the first screen in the function. Some of the ranges are self-expanatory, such as Vendor range, check amount etc (which select or ingore vendors).

In addition, you can select only specific invoices for each vendor based on the date fields at the bottom left of that screen. The field called 'on or before' will only select invoices with a due date (not the invoice date) 'on or before' that date. So if there is an invoice due in 30 days, it will not be selected for payment (without other controls) if it was posted in the last 29 days. There is also a date field which will ignore invoices where early payment discounts apply.

The first thing to look for is the due date of the 2 invoices not appearing for that vendor, and compare to the 'on or before' date. Another is to determine if either or both of those invoices have been put on Hold via Payment Control (also under the Payments menu).
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You may be aware that on the second screen of Print/Post Checks, there is a list of all the invoices that have been selected to pay, based on the criteria on the first screen. Clicking the Generate button is equivalent to printing the Pre-Check Register in terms or refreshing the list, so you can more easily determine if a particular invoice is to be paid and if so, if you want to pay it in full or not.