This is literally the only thing I can think of as to why he's not been sacked yet. I don't think it's anything to do with affordability - the cost of relegation is far more damaging than paying the price for firing Rodgers right now. I sense the club just don't want to be managerless. There were rumours that the 'sacking' of Rodgers was made more complicated when Potter went to Chelsea, which indicates to me that we were gunning for him.
I can't think of any other managers that survive getting thrashed every week, heading into October with no wins in any competition (a penalty shootout against Stockport really doesn't count), and conceding 4+ more times in 3 of the first 6 games this season. Totally embarrassing. Last season's errors don't appear to have been rectified i.e. defensive woes and set-piece shambles.
Rodgers is clearly waiting for the sack and his big payout.
Even sacking him and having a caretaker manager in place will help - just get the incompetent fool out of our club and give us all a bit of fresh air and belief. He's totally stank the place out and sucked the life out of it.