Man United are not very lucky when it comes to managers after Alex Ferguson retired. They keep changing them every season or two with no visible effects.
Now the latest rumours are they are considering Gareth Southgate, but Ten Hag is almost guaranteed to keep his job until the end of the season.
I realize that the cycle of football is getting faster and faster, and the patience of teams with their coaches is not as much as before. Purification happens faster and requires coaches to show immediate results, instead of building from the ground up gradually as before. Southgate is still in position with the England team, it is very hard for him to move to lead Mu.
There's clearly something wrong with United's attack, they've only scored 39 goals this season, which is very low for a club of their calibre (for Comparison, Arsenal has 70).
I think the problem lies mostly in the midfield, not necessarily in the attack. Mu's midfield did not do a good job of connecting the defense and attack. Their midfielders are not in good form, especially Bruno Fernandes.
I don't think anything could save Ten Hag's position unless he manages to please the fans and club owners by winning against Liverpool, Chelsea and Arsenal.
The most feasible goal to keep Ten Hag's seat is to help Mu win 5th place, thereby having the opportunity to participate in the Champion League next season. Currently, they are 6 points behind the 5th team, Tottenham, a gap that is not too difficult to overcome. If they maintain their current form, they can achieve this goal.