Rules of running a football club:
Number 1.
Good managers are not that easy to come by (cf Newcastle, Tottenham).
When you've got one, stick with him until you are convinced he's not one, and be patient, even when the less cerebrally endowed of your fans are baying for his sacking (cf Manchester United, Everton).
Number 2
Sometimes you need to get rid of a manager whom you once thought was a good one, but are now having some doubts about. Here are some guidelines.
Be patient, always. There is too much random chance in football to react to every result, or even every season. It is better to give a manager one season too many than to repeatedly give managers one season too few. Stability will serve you well in the long run.
You will know when to part company with a manager because you will see that there is no foundation for the future and that things are going in the wrong direction for a prolonged period of time - this period should be an absolute minimum of one season unless utter disaster beckons.
Any discussion of sacking Rafa is utterly ludicrous given that we are one of the best half dozen sides in European competition, we are second on goal difference in our domestic league in mid January and the first shoots of his youth development programme have started poking through at first team level (ie Insua). We have a good half dozen top/world class players whose futures would be under question immediately if Rafa left, especially as his likely destination would be Madrid.
Noone can guarantee number 19 this season, next season or ever, whether Rafa stays or goes. We are competing against very good, very expensively assembled sides. I honestly think, though, that anyone who genuinely thinks sacking Rafa would be a sensible way to progress Liverpool Football Club is a moron in the true sense of the word.