Fans opinion will matter a lot when he will be regularly booed.
When you finish outside the top 4, the board is not happy either as their bank balance is not increasing so they will also be more inclined for change.
As for you looking at Liverpool, I'd point to UTD and tell you to look at them. They haven't done too bad, have they? Why do we keep looking at the failures of others to justify not making a change? Why not look at others success? We have played the scared to make change card many times.. it's time for a change.