The idiom dog days traditionally refers to the hottest period of the late summer. It has a long and interesting history. The Romans referred to the late-summer period as dies caniculares, literally meaning Dog Star days, out of the belief that the summer heat was caused by the proximity of the star Sirius (the brightest star and part of the Canis Major—Large Dog—constellation) to the sun during these months. This belief may have come from the Greeks or Egyptians.
For the Romans, the dog days fell between July 24 and August 24. This is still roughly the period denoted by dog days in modern use, but the term is often extended to mean either the late summer generally, any waning stage, or any period of stagnation or languid activity.
In its traditional use, dog days refers to the hottest period of the late summer. It does not need to be capitalized or placed in quotation marks. For example, these writers use it well:
No one expects as much play during 100-degree dog days in August as they get in May and June. [Southern Pines Pilot]
But he’s confident that if the work ethic he exhibited in the chill of winter can be duplicated through the dog days of summer, Toronto will have plenty to cheer about. [Norwich Bulletin]
Because the dog days of summer are typically slow and languid, the idiom has been extended to mean a period of stagnation—for example:
The dog days that follow the 2011 NBA All-Star game are good occasion for owners and players to take the pulse of their league. [Sports Central]
But that didn’t make much of a difference in the U.S., and the confused supernatural thriller died at the box office during the dog days of winter. [AV Club]
And dog days is sometimes used to refer to the waning days of seasons, months, or other periods that are not summer—for example:
Last December, during the dog days of another bad season for his Cincinnati Bengals , T.O. laid it out on his talk show. [Dime Magazine]
Even great teams lose three consecutive games as they slog through the dog days of January and February. [USA Today]