The season in Antarctica generally runs from November to March, during the austral summer when the temperatures rise and the sea ice breaks up enough for ships to access the Antarctic Peninsula, the part of the continent that stretches closest to the tip of South America. In my opinion, there is no "bad" time to visit Antarctica during these months. It is there, it is accessible, and it is stunning.
I have had many a traveler tell me that they only want to visit in December, or their sister's cousin's brother told them they should only go in January and that they should at all costs avoid March. After taking a voyage that spanned the first two weeks of March, I must wholeheartedly disagree with whomever is spreading these rumors.
November is a wonderful time to visit if you are looking for pristine white icescapes. December and January are ideal to witness the penguin chicks hatching and take advantage of the most daylight hours, though these months are the most popular, therefore these cruises see the highest price tags and sell out first.
The end of February into March is an excellent time to visit Antarctica as well. First, because it is the "end of the season" and not peak travel time, you will find that price points are lower on cruises. More importantly, this is the perfect time for wildlife enthusiasts. Penguin chicks are now adolescents and are abundantly curious, much more likely to approach you (do not approach them!) and interact. Whales have increased in numbers and sightings of whole pods is frequent.
When you're considering your trip to Antarctica, don't discount late season! You won't regret it.