EV-CPO (as well as the other inventory sites) do not have a real-time/live feed of the price changes published by Tesla. So if there is a significant price reduction on the Tesla site, and the car is sold before any site has a chance to capture it, then no, those kinds of price reductions won't be captured.
A subscription gets you the most up-to-date information possible, but it's still not real-time. It's close to real-time as possible, though. Alerts are sent out immediately upon price changes via email or SMS. You can sign up for the two-week trial to try it out.
Why? Since the start of the CPO/Inventory program, Tesla has always withheld listing or posting every car for sale on their public facing website. I did not see the thread that was deleted, what was the content and why was it deleted? Anyways, it's conceivable that the OAs are also withholding price reductions before they are published online. Or alternatively, it's just a delay in the process that pushes the internal price changes to the online portal and they aren't withholding price reductions intentionally.