Yeah, I agree that the 'taking away stuff' issue can be a bit difficult, but it *is* one of the core MC moves (take away their stuff).
And I've been thinking a lot about the not taking away the thing that makes a character cool issue as well. I think that with that, certainly, nothing is *immune* to degradation, decay, et cetera. I think that is just an injunction to think about *why* you're taking stuff away in the first place, which should always be to serve the principles (make AW seem real, and make their lives not boring). So, if taking away even something cool would seem real and not boring, then yeah, that's what you do. On the other hand, don't exercise your ability to take things away just to do it. With the hardholder, his life would be pretty boring if you don't screw with his hardhold (I'm playing one right now, and my MC frequents these forums, so I may regret this :) ).
By choosing a hardholder character type, a player is saying "dealing with the issues of being a leader with an external powerbase is interesting to me". Now, sure, part of it is probably "it would be cool to have a gang and wealth and do stuff with that" but hopefully it also includes "I realize that shit's gonna happen to my gang, people are gonna challenge my rule, and most of the problems that affect everyone as a group are going to affect me as an individual double so".
I'm getting a little philosophical, but my main point is that the "don't take away what makes them cool" isn't an invincible decree, it's a reminder to make sure your decisions are based on what's most interesting and least boring. So, if you have spent a campaign working up a character's lucky rifle and how central that is to his identity, it better be a damn meaningful and cool event if he loses that rifle - it should just get run over by a truck because he flubbed an act under fire roll.
Which brings me back to one of the most important things about when it's "okay" to take stuff away. The rules tell you this when they say to "make as hard and direct a move as you like". It still has to follow from the fiction, but if circumstances warrant stuff getting taken away and somebody, say, fails an important roll, well you certainly can lay waste to important things - that's your permission. So, it'd be pretty damn hard and direct to say "hey, half your hold is dead!" so you probably don't want to do that when you haven't been setting that up with other moves.
As for taking away advances that characters have bought, my gut feeling is that those should be a little bit safer, but not invincible. Like with what I was saying about hardholders and so forth above, investing advances into an external thing that can be taken away, rather than a move, is saying at the same time "I think this thing is cool and want it to be part of my character" but it's also saying "I fully accept problems associated with this item, and will find them compelling, since its important to me".
All of the above is 100% my personal take on things, so take with as much salt as you find appropriate.