I guess in part its going to depend on what you mean by defeat. They may have suffered setbacks during the Jihad but ultimately won of course. Are you looking for the setbacks as well (I'm pretty sure they had setbacks. They lost at some point right?)
Basically. I suppose I have two motives here.
The first is that most factions have some spectacular defeats or overall maulings in their history, and those are often some of the most dramatically compelling parts in their history. The Wolves have the Refusal War. The Falcons have Coventry. All the Inner Sphere houses have taken it in the teeth before. The Bears don't seem to have anything like that?
Jellico might be right in that the Bears tend to have such dramatic scenarios? When they win, they do so by being patient, conservative, and picking up the pieces after other factions flame out; when they lose, it's a gradual grinding-down over time, not something exciting. The invested Bear player doesn't face horrible disasters, but neither do they get great moments of glory. So perhaps I'm looking for stories that the Bears just don't tell.
Secondly, though... broadly speaking it's that I generally find it harder to run games or stories where the players take the perspective of the obviously stronger faction. If I were running a game where the players are Davions, I wouldn't set it in the Fourth Succession War. If I were running a game where the players are Kuritas, I wouldn't set it in 3145. Not many people enjoy being a bully. It feels more exciting and interesting, to me, if the players are in some way vulnerable or face a great risk.
Naturally, with a perspective like that, it helps if the factions I'm considering often face conflicts where it seems like they might lose, or where the cost of victory will be high. Scenarios like this are often rarer with the Clans, but they do occur. Are there scenarios like this for the Ghost Bears, where the odds are genuinely against them? From the outside it can seem like the Ghost Bears have just marched in, consolidated, turtled, and then whenever someone pokes them, the Bears respond with heavy force... and they almost always win.
So - given the popularity of the Ghost Bears; as far as I can tell they're one of the most or even
the most beloved Clan - I was wondering when and where the Bears have been in desperate straits. What are the Ghost Bear wars where the Bears seem vulnerable or in danger?