Not quite sure it is that difficult to advance the gate status on FLY in a normal way tbh, but yes unfortunately quite a few gate staff seem to be incapable of even the simplest of tasks which then leads to gates going from "Gate Open" to "Gate Closed" in a matter of a minute.

As cws notes, if the departure is not showing as delayed on the BA app, that is the usual indicator you do need to get to the gate on time, and boarding may have started even though it still shows "Gate Open".