In spite of signs that say ''Always Open,'' 1,221 Denny's restaurants around the United States will close their doors on Christmas so employees can have the day off.

But some of the restaurants have not had locks for decades because of the always-open policy.

At others the locks were never used and the keys were lost. New locks are being installed at about 700 restaurants, said Joe Herrera, director of marketing at TW Services, the Denny's parent company, which has its headquarters here.

Mr. Herrera said the closing ''will cost us about $5 million in sales'' but added that many of the 60,000 employees were so grateful that they sent cards and letters to their employer.

They will not lose a day's pay. Mr. Herrera said, ''We just feel we spend 364 days a year taking care of other people's families and for one day a year we want to take care of our own.''