I dont think they sack him, he may well walk away, but wont be sacked.
Rightly or wrongly (Wrongly IMHO) there are enough mitigating circumstances to keep him post this season & you can make a case for why they might bounce back.
I'm not sure I entirely see it this way.
In the abstract I tend to agree. He has enormous stock amongst fans, though to be honest quite a few of them are turning on him now, and others are openly questioning him. 2 months and 12 games more with a lot of defeats would be bruising for him. I mean if he can consolidate at over 1 point per game, he might be able to limp on from the fans perspective, but anything less than that and I reckon there will be open revolt.
The problem for him, in honesty really comes next season. I think a lot of forgiveness from fans is that everything just goes back to normal and they win the league next season. As I think I put to Dave earlier, I can see a world where he improves from this form (I can't imagine a world where they are a point a game unless FSG panic and issue a firesale) but I am also not sure they get to 2 points per game. I don't think it will be good enough for a log of fans.
We are beyond the point now where we discuss is this a crash, or whether there will be a longer term impact, but it's really a case of how long the impact goes on for and how severe the current dip will go. You also have to throw in, I really don't think there will be much money for any sort of a rebuild come the summer. If there wasn't money in January, relying on CL money etc, there won't be with no CL and potentially no European money full stop.
The other cavaet in this, is it's ultimately not the fans who decide. I think the owners will look at his myriad of outbursts and digs, his insitence on two new CB's that he hasn't played, the crying for Koulibaly which was never realistic, the crying for Thiago who he has broke the bank for with wages and has badly flopped, and you start to say a collapse from 1st at Christmas to say 8th at the end of the season is just not acceptable.
They are almost certainly going to be looking at their biggest gap to the leader since the Hodgson days. It may even be the biggest gap in PL history (and in honesty since we all started watching football, as they were never far off from the 70's onwards). It took them 7-8 years post Hodgson or general big forward momentum and big spending (relatively so) to get to that point. I honestly think they are at that point, where they are 6 or 7 years off challenging again, and that assumes they start making the sort of ruthless calls FSG made back in 2012. I'm not sure any of them have come to terms with this reality at all.
In honesty, he's very lucky this collapse happened not a year earlier otherwise he would probably be gone now. Reminds me of Houllier 03, who they limped on with, with seething resentment from the fans, and in the end only messed up another season in the process.