We have been in this situation before, most recently with Rodgers.
I have it on very very good authority that over the Xmas period of that relegation season, the Board wanted to remove Rodgers, but Top stalled citing that the appointment was made by his father and it would be a dishonour to sack Rodgers at that time. If we had done so, we may have saved our season.
We find ourselves in a similar situation now, and I hope that we have learned the lessons of history!! I'm not optimistic that time will tell, so you may be right!