They might chose to remain apart because the colonies did not really have that much in common in the first place. While all the colonists spoke English, and the vast majority of the residents at that point (~1790) were of English or Scottish origin, the economies of the states were dependent on different things.
Characteristics of the Colonies
New England's colonies were based on fishing, whaling, shipbuilding, and shipping. They were heavily involved with the non-English colonies in the Carribean, as shippers of food to the plantations there and processors of molasses (into rum). There were basically no slaves in New England (less than 4,000, about 3/4 of them in Connecticut). The population of New England in 1790 was just over 1 million.
The middle colonies (NY, NJ, PA, DE, and MD) were sources of the food that the New Englanders traded, and also furs. Furs were the primary product of the interior United States and they flowed through Pennsylvania to Philadelphia, or down the Hudson to New York. There were some slaves in the Middle States; about 150,000, 2/3 of them in Maryland. Maryland is often considered a slave state, but it is the only 'traditional' slave state whose slave population dropped after 1790. Whereas the number of slaves in the US tripled between 1790 and 1860, it dropped by 10% in Maryland as the state shifted away from the plantation economy and Baltimore came to more closely resemble Philadelphia as a manufacturing and shipping hub. The free population of the middle states was 1.2 million.
The South sold cotton, tobacco, and indigo. Since the south's trade was more lucrative and population of free whites was MUCH smaller, the south had no incentive to start manufacturing, whereas Philadelphia, New York, and Boston had manufacturing economies as advanced as anywhere outside England, even as early as 1800. Slaves were of course plentiful in the south, making up close to half the population. The free population of the south was about 900,000.
Economy pulled the country in different directions.
The South would have wanted to maintain ties with England, since that was the richest country in the world and the primary customer for southern cotton and also indigo.
New England, on the other hand was basically in competition with the British shipping and shipbuilding industries. The New England colonies would have been geopolitically advantaged by an alliance with the Spanish colonies in the new world, a huge market for New England manufactures and shipping. At this time, Spain had little manufacturing and a small merchant navy.
The middle colonies would have been been somewhere in the middle (lol?) not being especially advantaged or disadvantaged by association with England. As the only net food producers of the New World, they would benefit most from the growth of other colonial empires that they could feed (perishable food being difficult to ship across the Atlantic).
Economic difference caused a potential for separation between the states. The impetus for separation could be one of the below:
The Elephant in the Room
This was of course slavery, the issue which came the closest to actually splitting the nation. In addition to the actual civil war, there were tensions around the 3/5 Clause of the Constitution, the Missouri Compromise, the Nullification Crisis, the aftermath of the Mexican-American war, etc. Had the issue gone to war during, say, the Missouri Compromise of 1820, its entirely possible, the New England, Middle, and Southern sections of the country would have gone their own way. This is especially true since the New Englanders voted differently from the rest of the nation in the 1820s. New England provided 31 of 34 dissenting electoral votes against James Madison in 1816, and the only dissenting vote in 1820. NE voted 51 of 51 for John Quincy Adams while the rest of country voted 30 of 210 for him in 1824. In 1828, NE went 50/51 for JQA, and the rest of the country 33 of 210.
The other event that could have split the nation was ratification of the Constitution. It was a heroic effort on the part of many of the founding fathers to convince state legislatures to ratify. As it was, two of the original 13 states (North Carolina, and Rhode Island) had not even ratified the Constitution by the time George Washington too his initial oath of office. Many of the largest states,had close votes: 187-168 in MA, 89-79 in VA, 30-27 in NY. Rhode Island rejected the constitution in a referendum, and North Carolina's legislature voted once against ratifying before coming around later. Incidentally, that means that neither state nor NY voted in the first presidential election. Imagine if you weren't allowed to vote and then Hillary or Trump (pick who you hate more) became president!
In any case, if ratification was a close call in many places, and could have failed. In that case, it is not at all clear what would have happened, but three regional nations, or 13 individual nations are both possibilities.