Some companies are really big and well known so they may not fall fast, or even for a long period of time, but it is possible for them to fail. Just because a company is rather large does not make it incapabale of failing if anything the bigger they get the more is expected of them.
I do not believe any company is considered too big to fail. There have been numerous companies that are considered "big" companies that have failed or are in debt or going bankrupt. Blockbuster, which was a nationwide chain has recently closed all of its stores and it was considered a big company. I have no doubt that other corporations that are large could fail as well.