Last year, I had two 100+ buy-in downswings. This year, I started off the year going down around 90. On carbon, those swings don't hurt as much because of the leaderboard bonuses, but they still happen, and you need to be prepared.
Regarding that hand, calling with A9+/KQ+ and any pair would be a big mistake.
Take a look at this:
Although BTN probably isn't shoving any two here, I put that range just to show how tight we have to be. We can only call here with the very top of our range and part of the reason why is what you said, the BB has 25% of his stack invested; he's going to be able to call the BTN shove wider. If we call, we give the BB the opportunity to fold and then we face off with the Big stack for our tourney life.
When we fold, we give the BB the opportunity to call and get knocked out. That's what we want. We need to keep the pressure on the BB in this scenario.
This is just one scenario and things would change if we had even stacks with the BB, or maybe slightly less chips, but the point I'm trying to make is ICM really dictates how we need to approach these types of spots. Calling with a hand like AK here would be a no-brainer to most people, but we don't gain enough equity when we do, so folding is the right move.