How do you play when you face several opponents that frequently goes all-in?

I mean, what it effectly means is that any hand you plan on playing you should be willing to go all-in aswell on? Say you got AA and start with a raise, then a reraise and suddenly the other guy is all-in, then if I call it will be luck deciding the outcome (with me as a favourite preflop) but it's a gamble, if I fold I'm giving up say 30% of my chips even though I have the best hand pre-flop.

If you say I shouldn't go all-in and gamble, the problem is that I already invested good money in the favourite hand and it doesn't take many situations like this in a sng before my chips are eaten away. Should I just sit back and fold even premium hands if I face any competion keeping the costs low in the early rounds and start gambling later on?

Hope you understand my problem.