This happened to me a few years ago - 3 hrs to go the sale fares disappeared while the big clock continued to count down. Of course no BA help available after 8pm so nothing to do. I took screenshots of the whole sequence, availability etc so I'd have some evidence....but booked on VS who had a corresponding sale which was still active.

When I called BA the next day I got all the usual "all the available sales seats were sold on that flight", "sir, those booking classes were not available...." etc etc. After I pinged the Executive Club on Flyertalk and sent over all the screenshots they came back later in the day and said they would have refunded the price difference if I'd booked the higher fare but as I'd already booked with VS there wasn't anything to do.....

It's pretty slack on BA's part that this keeps happening and if there is going to be a big countdown clock then you are perfectly entitled to expect that you will get the sale fares right up to the end time.

VS have a very simple solve for this.....their sales prices remain available on the web for a couple of hours after the sale is meant to end.