The reason I believe that Manchester United coach job is at risk is because when you talk about dismissing a coach it is always done at the beginning of the season if the club feel that the coach cannot lead them to their target end. Any club that refuses to dismiss their coach in the early time of the season will definitely get wrong result even if they later do so. This is because the New coach would complain that there is actually no time to turn around the poor performance and would likely request for a new season. This might plunge the club to a situation of dismissal and hiring of coaches just like Chelsea.
It is therefore important for Erik 10 to prove that he is capable of remaining in Manchester United as their head coach. There is some kind of revamp of the management of Manchester United, so he should understand the body language that it is no longer business as usual.
Also, other teams do this, meaning that if they are not happy with their coach then they will fire them early into the season and will hire whoever is left. So, if you decide to get someone else at the middle of the season, you will be forced to get someone who has been just fired, and that's usually not a good way to continue your teams future.
The best case would be just making sure that you deal with whatever problem you have with the manager at either very early into the season or after the season ends, there is no middleground. I get that United may not be happy with the results they got so far, but I believe losing to Liverpool was expected, only one bad game so far, and they decided to work with him this season as well, so it shouldn't really be something they decide this quickly neither.
I think they should give him time until November, by November if he looks and then fire him and get someone else, it's still early in the season when you talk about November, so it shouldn't be an issue to find someone else. I have no idea who they would hire in that situation, it wouldn't be a simple decision but I think it would make sense on the long run and they should be quite happy with what they have.