There are a few things that would need to happen for Amazon to go out of business.
First, people would need to stop shopping on Amazon. This is the company's bread and butter - without people buying things on the site, Amazon would quickly go under. To get people to stop shopping on Amazon, a competing website would need to become more popular and offer better deals than Amazon.
Second, Amazon would need to have a significant drop in its stock price. This would make the company less attractive to investors, and would make it harder for Amazon to raise money to keep the business going. A drop in the stock price could be caused by a number of things, including poor earnings reports, bad publicity, or a general decline in the health of the economy.
Third, Amazon would need to start losing money. This could happen if the company's costs increase faster than its revenue, or if it makes a series of bad investments. Once Amazon starts losing money, it would become harder and harder for the company to stay afloat.
Ultimately, it would take a combination of all of these things to cause Amazon to go out of business. If any one of them were to happen, it would be a serious blow to the company, but Amazon would likely be able to recover. It would take a perfect storm of all of these factors to cause Amazon to go under.