As i said in Liverpool discussion thread i can't see him being sacked anytime soon. Yes they have a bad squad and their general play is not good but to think that he will be sacked at this stage is just a wishful thinking from Liverpool supporters.
He is now quite a long time a manager of Liverpool and current squad is really his creation. The owners backed him with a lot of money every summer and they did the same last summer. If his sacking would be even a little possibility i think the owners wouldn't backed him with this much money as they did last summer.
Now he spend around 300m pounds, this is a lot of money, and their owners will give him as much time as possible if he can turn things around with this squad. They know that if they sack him the next manager will want to completely rebuild their squad once again which would cost a lot of money. The similar rebuilding job like we had is strong possibility if they decide to bring new manager. I don't think they are prepared to do that after how much money Rodgers already spend, it is not like us when we didn't spend a lot for a long time and Glazers knew that sooner rather than later they will need to show the money, Liverpool owners had already showed the money and another rebuilding job is the last thing the would want.
As for Rodgers he looks like a parody of himself and is totally lost. He clearly don't know how he wants to play with changing the formation everytime they play badly and he don't really know what players fit his style of play, their squad is one of the worst Liverpool teams i have ever seen and this squad is his creation.