When Does "Star Trek: Enterprise" Season Four (2004) Take Place?
"Star Trek: Enterprise" season four is a science fiction television series showran by Manny Coto that released October 8th, 2004. So when is "Enterprise" season 4 set?
It takes place on the fictional Star Trek timeline in the year:
We know this because very early in season 4 episode 4 "Borderland" Captain Jonathan Archer records himself saying, "Captain's Starlog, May 17, 2154. We've crossed into the Borderland"... So it seems to be May of 2154 AD at the season's beginning.

2154 AD - 2155 AD
We know this because very early in season 4 episode 4 "Borderland" Captain Jonathan Archer records himself saying, "Captain's Starlog, May 17, 2154. We've crossed into the Borderland"... So it seems to be May of 2154 AD at the season's beginning.
Then, very late in season 4 episode 21 "Terra Prime" (2005), the second-to-last of the entire series, Captain Archer makes another record saying, "Captain's Starlog January 22, 2155. Enterprise is returning to Earth." So it's certainly January of 2155 AD at the end of the season.
Although the famous "stardate XXXX.X" captain's records that open most episodes and some films were mistaken for years on the Gregorian calendar, there is no one-to-one relationship between them. As identified in the biography "Gene Roddenberry: The Myth and the Man Behind Star Trek": "They marked off sections on a pictorial depiction of the known universe and extrapolated how much earth time would elapse when traveling between given points, taking into account that the Enterprise's warp engines would be violating Einstein's theory that nothing could exceed the speed of light. They concluded that the 'time continuum' would therefore vary from place to place, and that earth time may actually be lost in travel. 'So the stardate on Earth would be one thing, but the stardate on Alpha Centauri would be different,' Peeples says." so they are relative to long distance travel and not an absolute calendar. HOWEVER, actual years on the Gregorian calendar began to be used later.
Additionally, season 4 episode 1 "Storm Front" and episode 2 "Storm Front Part II" involve time travel to the year 1944 AD. The year for the time-travel portion of the two episodes is clearly identified when Captain Archer asks, "What year is this?" and Alicia Travers simply replies, "It's 1944." during "Storm Front".
Finally, the series finale, season 4 episode 22 "These are the Voyages…" (2005), functions as an epilogue to the series, primarily taking place in 2161 AD but told with a frame story that takes place in 23?? AD.
It is the earliest chronological TV show in the Star Trek universe and can be watched at its timeline point or as an extended flashback after "Star Trek: The Next Generation" (1987).