This is a variation of the boy cries wolf too often & villagers get weary & won't come to help when the wolf really arrives.
Satire is on the mass media. Mysterious phenomena are observed every July/August in various parts of US over several years - transparent domes that kill anyone who touches them but vanish by the time news reporters reach, mysterious spheres floating around that are seen by one group but cannot be verified later, ...
First year, the media milks it to the hilt with silly jokes of incredulity. Next year, fewer people are attracted towards the news, & media is forced to not play along far. Forth year, no one believes in the phenomenon but this time it's the real Martian invaders!
- Title, "silly season", refers to summer of US; author specifically mentions July & August. This apparently is the season for baseball (or was in 1940s) - apparently a counterpart of India's domestic Twenty20 cricket season. This is supposed to be the time of the year when few newsworthy things happen; hence the media grabbed the news during first year.
Looks like summer months differ across latitudes, even in the northern hemisphere. India's summer, e.g., ends in June.
Fact sheet.First published: F&SF, Fall 1950.
Related: Stories of C M Kornbluth.