The way I see it, in deciding whether to sack a manager there are two types of error you can make. Call them Type I and Type II in the usual fashion.
Type I, also known as false positive, occurs when you make an unwarranted sacking. You decide to pull the trigger on a guy who would have accomplished great things here if not for the sack, or will accomplish great things in his next destination. The downside of Type I error is the possibility of missing out on a great manager in the making. Seems quite straightforward so I'm not elaborating further.
Type II, also known as false negative, occurs when you don't sack a manager that should already have been sacked some time ago. The downside of Type II is the damage you have to endure by sticking with an unsuccessful manager. Financial losses, reputational hits, and similar stuff all belong here. This also seems straightforward.
Now, how do the downsides of these respective errors compare in the case of Ange?
What about the possible downsides of Type I, a.k.a sacking him? How big is, or should be, the fear of missing out? What are the chances of sacking him and then him turning out to be the one that got away for example? He's 60, even Celtic was a big jump in his career let alone Tottenham, and he has already spent enough time here for us to get a sound idea of who he is. Sorry, but nothing tells me that we would regret sacking him years later down the road. Even if his successor(s) turn(s) out to be not so great.
What about the possible downsides of Type II, a.k.a keeping him? We're already witnessing them. Injuries that have at least something to do with him is one. Financial loss and loss of prestige caused by missing out on Europe next season is another, whose repercussions will be felt more acutely during the summer transfer window. These downsides are quite concrete, and are already felt. Unless there's reason to believe that they're worth enduring for the greater gains in the future, there's no reason to keep enduring them. And I don't see what those gains would be under Ange.