The OK button is the normal behavior for the SO Inquiry screen. I'm not sure if it's the cause of randomly disappearing orders but worth trying the suggestions.
I have seen a script scenario where the Inquiry screen pops up but wrong title (says Sales Order Entry instead of Sales Order Inquiry) but orders weren't getting deleted.
If you run out of options you could actually create a post-delete script where you could log a bunch of info to the Activity Log or a CSV file such as the user, date, time, order No, the Start Program (eg you could see Sales Journal Update which is a normal delete or another place that you're not expecting a Delete).