The Mishkan was located in Shiloh for hundreds of years. According to the Gemara (Megillah 9b, Zevachim 112b), Shiloh had almost the status that Jerusalem would later have: the mishkan was given stone walls; pilgrimage from the entire country came to Shiloh; sacrifices in other places were prohibited. But early in the life of Shmuel haNavi, Shiloh was sacked by Philistines and the mishkan destroyed. This was a momentous event, perhaps similar to the destructions of the two Temples. Israel's first request for a king came shortly after the destruction, presumably due to the terrible military weakness which they thought was caused by disunity and lack of a strong leader.
Sefer Shmuel Alef, chapter 4, describes how Philistines captured the Ark of the Covenant which had been taken into battle, and how high priest Eli's family was almost wiped out. But for some reason, the destruction of Shiloh is omitted. Later in Tanach (for example Yirmiyahu 26:6) we find passing references to the great destruction which took place. It is from these sources and archaeology that we know that there in fact was a destruction. But there is no mention whatsoever in Shmuel Alef. Chapter 4 spends a lot of time saying how each of Eli's children died, and how contemporary events are reflected in the name of his grandson ("I-chavod"), while omitting the most important of those events. Why?
To answer this, I think we have to look at the overall focus of Sefer Shmuel. I would argue that the book deals not with the history of Israel per se, but particularly with several of Israel's leaders. Most of the book focuses on Shaul and David. We hear how Shaul was selected, his potential as king, and how he then blew his chance and had the royalty taken from him. After that the book focuses solely on David: how he became king and how he was a better, though perhaps flawed, king than Shaul had been. It would not be farfetched to say that the entire purpose of Sefer Shmuel is to justify the choice of David's dynasty and confirm that the Mashiach will eventually come from his offspring, not Shaul's.
In the first few chapters of Sefer Shmuel, Shaul and David and their rivalry have not yet been presented. But a very similar dispute over authority does appear. Eli, the established priest in Shiloh, loses his position as spiritual leader to the charismatic Shmuel. Just as the bulk of the book focuses on justifying David's political authority in place of Shaul, I think these first chapters focus on justifying Shmuel's place as spiritual leader in place of Eli.
Thus, since the purpose of the book is to present personalities and not national history, events which do not directly relate to the personalities can be omitted. It is necessary to tell about the battle in which the Ark is captured, not only because it shows how low Israel has sunk under Eli's tenure, but also because it directly leads the death of Eli and his children. Their death, of course, must be mentioned for the same reasons.
But once we know the fate of Eli's family, there is no need to recount events which took place afterwards. We already know that Eli led the nation to defeat. If the destruction of Shiloh were to be mentioned once the focus of the book had shifted from Eli to Shmuel, we might mistakenly think that Shmuel was responsible for that misfortune. In order to avoid such an impression, the destruction of Shiloh is left out entirely. There is no danger of over-justifying Eli (apparently a nice guy, but a terrible leader), because enough negative events have already been mentioned that we know he was a failure.