You cannot get busted if you are not all-in. So, in a tourney where you cannot rebuy, you want to avoid allin situations as much as possible. That said, you will have to go all-in on occasion. You cannot keep folding to pressure. Just pick your spots -- preferably against a player looser than you, preferably with a premium hand. Then cross your fingers and hope you are lucky, because all-in means you have cast your fate to luck.
Some tourneys, luck will be with you and it feels smooth -- you get a lot of premium hands and you win those showdowns -- until the last one. Others, your hole cards are abysmal for ages and you try to make do with positional play and raising the mice. Those tourneys are rocky horror shows.
You may not want to listen to me. I often enough cash, but seldom place high. Depends on what you want. (Personally, I want both, but don't seem to get there.)
The best players do not win every tourney they are in. They do not cash every tourney. There are few people who cash in 20%+. 15% cashes is pretty good. That means 85% of tourneys played are dead losses. Accept that fact. A lot of tourney poker will have you on the rails a lot of the time. It just is.
The difference, though, between the best players and, say, me (my current OPR stat for 2009 on NLHE tourneys is 19% -- not accurate but ok -- looks good but in actuality does not put much cash in pocket) is that, when they cash, they place a lot higher. And, overall, they make more money, more ROI, on the tourneys they cash in.
The trick is to place high regularly and cash in 15% or more. I have not figured out how to do that yet. But it clearly involves a combination of aggressive play and safer play. Some people can fold that AJ easily under pressure, some cannot.