The answer I get is because the manager is bad at their job, because their team keep losing. But that defies the most basic logic of sports. Football is a zero sum game; if a team wins, the other has to lose. The better one team does, the worse the other teams would have to be doing to make that functionally possible. That's the entire point.
So why is a string of failures automatically attributed to bad management, if loss is an inevitable part of a game? That's like firing a manager of a Christmas card manufacturer, because the sale of cards lulls right after December. Note that I am not saying a footie manager has no influence on a game, or that a manager can't be bad at their job, its just that the win/lose model is the worst possible way to judge the ability of a manager.
The other thing as well is that it isn't even all that effective. A recent graph of win/losses of Dutch football teams showed that, whether or not a team replaces their manager after a string of losses, it doesn't really make a difference. Inevitably they will have an upswing, and this is often wrongly attributed to the new manager, much in the same way that we attribute failure to an old manager.
But if there is no logical reason for replacing a manager, why don't the most senior share-holders in these organisations keep doing it? They must know, surely? The answer most likely is that whilst they are perfectly aware the manager is largely blameless in most instances, the average football supporter isn't, and will loudly complain when their team is doing badly. Rather than risk their less than die hard fans migrate to a better performing team (and lose that delicious t-shirt revenue), the big wigs try to placate these folk by scape-goating the poor manager and promising a better performance with the next one. I am not sure which I find more sad - that people need to maintain this artifice, or that it tends to happen in most walks of life. If you think about it, there are many circumstances which in hindsight could have been solved by simply doing nothing about it and waiting for things to improve. But in most cases, people aren't allowed to appear to be complacent or uncaring, so they need to dive in and mess around, even at best it is a wasted effort.