High fuel prices can actually contribute to an airline doing well and making profits -- given proper fuel hedges, a good cost structure, pricing commensurate with costs and desired profits, and an efficient operation. All airlines (and, indeed, all transportation modes) will face this increased fuel cost -- the higher operational cost actually accentuates the opportunity for efficient operation, resource acquisition, and pricing over that of competitors. The only risk you run is potential underutilization of your capital; if you're smart you can mitigate the impact of this as well.
What you can't do is let your competitors set your price--you need to raise your prices to preserve a profit margin as your operational costs go up. Not doing this (as well as complex pricing schemes) have resulted in the demise of many American air carriers.