Obviously, there is no chance for Chelsea to be able to finish in the European zone even though indeed, when Pochettino was appointed as Chelsea head coach. So ya, at that time Pochettino really became a hope to be able to restore Chelsea's performance but unfortunately, what happened was that Chelsea remained just as bad and no big change occurred until now. Therefore, because at this moment Chelsea are still in the middle of the standings then of course, there is no chance for Chelsea to be able to recover for the rest of the season, because Chelsea still does not have a good squad and performance completely until now.
They created this crisis by sacking Tuchel and did not give the German coach a little more time. One season after winning Champions League with Tuchel, they sacked him and their crisis started from that decision.
Pochettino was chosen in the summer to end their crisis but till now, it seems he could not achieve big improvements with Chelsea. Again, if they don't want to wait, they will sack another and repeat the cycle. They must look at their squad that no longer have big star players like generation of Terry, Lampard, Drogba. Their current players are young and need time but of course, no guarantee with time they will become bigger star players.
I see it's more risky if Chelsea only look at results and ending of this season, to sack Pochettino. Let's give him not only this season but one more season, before making any decision on his job.