We kind of have the opposite problem to Utd's.
I'm sure they would love to sack Van Gaal now, but that would probably mean installing an interim manager. The interim manager would probably be Giggs, arguably the most successful manager in the clubs history. If he was to do well, maybe win the FA Cup, the fans would be calling for Giggs to be installed as the permanent manager.
The clubs owners clearly do not want Giggs as the next manager and they don't want to make a decision now that could ultimately pressures them into giving him the long term job, lets call it the Di Matteo scenario. The want emotion removed so they can make the best decision in the summer.
We on the other hand have a manager who is performing appallingly in the league but in Martinez's case, the failure to sack now could cause the long term problem. If he wins the FA Cup he gets the keys to the city, Everton do not sack manager who win FA Cups, they go down in folklore. But the vast majority of fans are terrified by a fourth Martinez season, it looks inevitable that this seasons league position will be worse than last seasons.
Liverpool were probably facing a similar problem with Dalgliesh. He was clearly not the right man to take them forward in the long term, but he was in an FA Cup Final against Chelsea in 2012. Win it and it would have been virtually impassible for the clubs owners to sack him.
So in Utd's case, it is probably the wise decision to wait until the end of the season because their interim could force the clubs hand.
In our case, it could be disastrous waiting until the end of the season. Martinez knows its the FA Cup or nothing. If he wins it, Moshiri will not be able to remove him, even if he wanted to. The momentum would be well and truly be behind Martinez, despite the dross served up in the league for the past two seasons.
We will still be an FA Cup semi final, even if we sack him now.