What version of Adagio Invoices are you using?
When a printed invoices is edited, this resets the print status back to Open for audit purposes. Ensure that invoices have not been re-edited. Perhaps check that no-one was in the batch when another user printed the invoices - the program doesn't allow this but it's something to check.
The only option in the Invoices company profile that would affect this is 'Post invoices without printing', which is likely not enabled at your site, and perhaps not desirable to enable.
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Regards,
Softrak Tech Support