The way this works is that there are 3 scenarios
1) Short delay - just a bit of app notification, usual timings apply, there may be an effort to bring down delays - more usually though delays creep out.
2) Medium delay - over an hour or so - BA sends out emails / SMS to those who have opted in for them to explain the delay, usually there is a sentence in asking people to attend the airport on the scheduling timings.
3) Delay goes much longer - BA then sends out a more tailored email / SMS where they would explicitly state that checkin can continue until xx:xx hrs.

Unless you are on 3) then it is what it is.