After King David died, he choose his son Solomon to reign. David had to deal with a rebellion from another son, Absalom: the dramatic and tragic family drama can be read starting here. GOD's victories through David would bring Solomon great riches, which would wrongly be used to destroy what could have been a beautiful long-standing empire.
Here's five reasons why within one hundred years everything would fall apart:
Marrying like a madman: Before criticizing King Solomon it's only right to mention that he began well and not just because of his father: for example he had the first Temple built, as well as a palace, but it is revealing that he built the palace built twice as large as the Holy Temple. He clearly had a good relationship with GOD in his early years (GOD spoke to him directly and came down during the dedication of the Temple he had built.) Despite this he disobeyed the Torah's words about marrying gentile women despite his father telling him "I am going the way of all the earth. So be strong. Show yourself to be a man. Do what the Lord your God tells you. Walk in His ways. Keep all His Laws and His Word, by what is written in the Law of Moses. Then you will do well in all that you do and in every place you go. Then the Lord will keep His promise to me. He has said to me, ‘Your sons must be careful of their way, to walk before Me in truth with all their heart and soul. If they do, you will never be without a man on the throne of Israel." And Solomon didn't just ignore the commandment, he married more women than any ruler before or after him. He married seven hundred women and had three hundred concubine. He married Pharaoh's daughter as well as women from Moab and Ammon (east of Israel), as well as from Edom (south-east), Sidon (north) and Hittites (whose kingdom had existed in modern day Turkey hundreds of years before Solomon.) These women were against the Torah for a reason: they lead him to idolatry.
Worshiping idols like a fool: When Solomon got older he did what would be un-thinkable for Moses and David before him: He build altars to gods from surrounding areas: what made Israel's culture unique was that it was strictly monotheistic--idolatry was punishable by death according to GOD's Law and yet here was the king of the empire doing it openly. Here GOD was blessing the King with wisdom and riches, and how does Solomon respond? By willingly disobeying GOD.
Rebels: After King Solomon began to build altars he faced rebellions: Hadad an Edomite, Rezon who became a warrior and ruler of the kingdom of Damascus, and Jeroboam one of Solomon's own officers. Both the Kingdom's of Edom and Damascus rebelled. But the final mistake that would officially end "The United Kingdom of Israel" would only be partially the fault of King Solomon.
Hardship and 'noble' indifference: During Solomon's reign he placed on his people a heavy burden, for this reason when his son, Rehoboam, succeeded him they said to the new king: "Your father made us carry a heavy burden. Reduce the hard work and lighten the heavy burden he put on us, and we will serve you.” King Rehoboam told them to come back in two days and inquired both of older leaders and young nobles who had grown up with him.
The two groups gave very different advice:
The older men told him: "If you will serve these people today, humble yourself, and speak gently, then they will always be your servants."
While the younger men told him: "This is what you should tell them: ‘My little finger is heavier than my father’s whole body. If my father put a heavy burden on you, I will add to it. If my father punished you with whips, I will punish you with scorpions.’”
When the time came to announce his response he told the people: “If my father made your burden heavy, I will add to it. If my father punished you with whips, I will punish you with scorpions.” Which lead to a rebellion, when Jeroboam (the rebel who fled to Egypt) returned, the people made him king of Israel.
And so everything fell apart and the United Kingdom fell from it's golden age; the remaining Kingdom of Judah was attacked by King Shishake of Egypt soon afterwards, then came the Assyrians and the Babylonians if the Kingdom of Israel and Judah had remained united with one organized military, one religion with one GOD, one capital and Temple it could well have lasted another five hundred years or so.
So what's the lesson to take from this?
1.) Obey GOD, even if you have strong desires and don't see why your actions are harmful.
2.) Don't be ungrateful to GOD and don't return His blessings with idol worship.
3.) Listen to people if they claim they need a break.
4.) Listen to the old folks, not young people.
Approximate land controlled by the Kingdom's of Israel (north) and Judah (south).
This image shows a record of Pharaoh Shishak's invasion, just five years after King Solomon's death.

