I've seen them go up sometimes, go down very rarely (mostly at unremarkable midrange hotels which notice they overpriced themselves compared to same-brand hotels in the same city), have the sale allocation sell out, but usually stay the same. That seems to depend mostly on how dynamic a given hotel's revenue management is, which can be observed during non-sale periods as well. The full gamut of approaches can be seen even within one city and chain, as various owners do as they please.

The first case is what riles me about the absence of notification, as by the time someone posts about it on FT, those hotels which adjust rates to demand have already bumped them up on the second day (Conrad Tokyo and to a lesser extent BKK comes to mind).
IIRC this year has been especially bad regarding email notifications. I seem to recall a few advance email notifications and some shortly after the sales started in the past.