The answer is yes. If it is past the settlement date and no extension has been created, then the contract is automatically dead.
I would caution about not extending, unless you have just decided not to sell. Your agent has done a lot of work to get your house sold, the buyer's agent has done a lot of work to get their buyers to the table, the lender is in place with a team of people doing the underwriting, etc., and the title company has also done a lot of work as well. So, if there have been hard feelings from either side, do consider that, while emotions are involved because this is your home, this is a business transaction that everyone wants to make happen. It can be hard to separate the two, but getting the house sold will allow you to move to the next step.