No
If he is winning then that is the most important thing. If he is losing then his job should come into question.
So if come end of the season he finishes 10th with an average record then we should replace him. If he loses another 4 in a row from now.then we have to replace him.
It's basing it on results and performance rather than knee jerk reactions. If we had lost yesterday, would I have wanted him sacked this week? Absolutely. Because it wouldn't have been one defeat, it would have been 5 in a row. However one win where he changed the team, style and mentality shows progress. As I say it is up to him to continue that or face the backlash for failing.