This post is based on this redit thread : https://www.reddit.com/r/lostmedia/comments/10hll81/partially_lost_the_melancholy_of_haruhi_suzumiya/
This entry is about the original 2004 manga adapted from the light novels by Makoto Mizuno, not the well know 2005 version by another author. Despite what sources may say, the manga has ever truely been fully found.
While the chapter 1-5 and is well known and available, but the existance of Chapters 6-8 are very under reported on. With even the fandom wiki only having minimal information about chapters 1-5 that were released in a tankoban, with many sources not even acknowledging their existence. The truth is there were 8 chapters released in Shonen Ace magazine with the 8th Chapter in the December issue being the last before this manga was cancelled.
So the way it goes is that the entire cancelled series (Chapters 1-8) appeared in the monthly magazine Shonen Ace throughout the year 2004, and Chapters 1-5 were released in Vol 1.
Progress so far:
Chapter 1-5 is available and chapter 7 has been found by a redditor leaving chapter 6 and 8 still lost.
Chapter 1-5: Found (Available in volume 1)
Chapter 6: Lost (Only in October 2004 Shonen Ace)
Chapter 7: Found (Only in Nov 2004 Shonen Ace)
Chapter 8: Lost (Only in December 2004 Shonen Ace)