Virginia was initially a powerhouse within the US due to its high population and large agricultural output. As more of North America became settled and became new states, and as those new states started growing their agricultural bases (especially in the South) that began to challenge Virginia's position. Meanwhile, the population of other states (especially in the North) grew as well, by birth and by immigration, and their economies grew too, with trade and new born industry rivaling agriculture for economic supremacy.

Consider population alone. In 1800 Virginia's population of about 800k was fully 15% of the entire nation's population. It was an even higher percentage of the population of the actual states themselves (excluding territories), which is why the state held 19 of the 106 (18%) of the seats in the House of Representatives, fully 1/3 larger than the next most represented state (Massachusetts). By 1840 the population of Virginia had increased by only about a quarter, to just over a million, while the US population increased from 5 million to 17 million, diluting Virginia's relative population from 15% to 6% and their share of representatives to 9% (21 out of 242 seats). By 1860 Virginia's population had increased by another 1/5th but again the US population boomed, nearly doubling to 31 million over that period. By then Virginia held only 4% of the nation's population, and 7% of the seats in the House (13 out of 183).

But this story is not the same for other states. New York went from a population of around 600k to nearly 4 million from 1800 to 1860, increasing its representation in the House from 9% to 18%. Similarly, Pennsylvania's representation increased from 11% to 14% (as its population grew by 400%). While Ohio went from being a newly admitted state with a nominal population to holding 11% of House seats with a population of over 2 million. Alabama and Mississippi similarly grew from nominal populations (of US citizens) to populations of 1 million and 800k (respectively), while Massachusetts tripled its population in the same period.

In short, through the early 19th century Virginia maintained a fairly slow pace of growth while other states and the nation grew rapidly and while many new states were added to the union. All of this vastly diluted the political power of Virginia in government. From holding nearly 1/5th of all House seats and 1/16th of all Senate seats in 1800 to holding only about 1/15th of House seats and about 1/32 of Senate seats by the 1850s.

Meanwhile, of course, there was a massive land grab and economic expansion to the West, which moved the center of gravity of America's agricultural base (as well as its slave owning/trading economy) from Virginia and the coast out to the cotton belt. While at the same time maritime trade and industrialization were taking off in the northern states. As mentioned above the populations of New York, Pennsylvania, Massachusetts, et al grew rapidly during the early to mid 19th century but their economies grew even faster. Between shipping (and ship building), whaling, fishing, international trade, textile mills, steel mills, railroad construction, and so on the economies of the Northeastern US states were rapidly modernizing and growing. Leaving Virginia behind.

At what point Virginia's power faded into normalcy is probably an open question, to some extent it was a gradual change. It is notable that the John Quincy Adams administration (coming into office in 1825) was the first time there was no one from Virginia in the executive branch (President or Vice President). After that point Presidents coming from Virginia went from ubiquitous to somewhat rare.

Arguably New York became the new center of the country (politically, economically, and culturally) sometime during the mid 19th century. Though you could make an argument about Ohio's political power as well (or Pennsylvania, or Massachusetts, etc.). And both states had more than their fair share of high profile politicians (including Presidents) on the national stage. However, the overall increase in the number of states, total population of the US, and the maturity of the country's institutions over that time frame meant that no single state could dominate the national political stage the way Virginia was able to around the turn of the 19th century.