Market Economy !!

I am unable to understand what kind of market economy is it. Every now and then a firm becomes bankrupt and US government comes out to help them. Recent rescue of the AIG makes it to §900 billion from tax payers money. Isn't market supposed to be resolving the issue of this economic crisis?
I am not economist, so I dont have an explaination, I just have an question. Let see how many more comes ...