Since 1980, in which years has the US debt-to-GDP declined and why? In other words, what were the factors in the reduction of the debt-to-GDP ratio?  Why did the ratio decrease during some booms and not others?
The time series for the debt-to-GDP ratio are available on the FRED wesbite: link to debt-to-GDP chart. I will let the reader download the data, rather than list the years here.

As for why it falls, it requires a good macroeconomic model. The reason being is that we need to explain both the fiscal deficit and the rate of nominal GDP growth.

Policymakers do not directly control the deficit. Faster growth means a greater tax take, less social spending. Meanwhile, capital gains taxes are determined by the hard-to-forecast changes in stock prices.

Nominal GDP (the denominator) can grow as a result of faster inflation, or faster real growth. The precise determinants of this have bee the subject of economic debates for decades. I obviously cannot answer it here.

One factor to keep in mind that the existing level of the ratio matters a lot. If nominal GDP growth is 5%:


you need a fiscal deficit of 5% of GDP to keep the ratio unchanged if the starting level is 100%,
you only need a deficit of 2.5% if the starting level is 50% of GDP.


If you look at the chart, the biggest fall in the ratio after 1980 was during the late 1990s. There was a brief fiscal surplus, and growth was relatively strong. There was a technology boom, along with the tech stock bull market/bubble that generated a lot of capital gains taxes. (The Clinton administration raised taxes earlier, which was also a factor in the surplus.)

(In a comment, you asked about the 2000s. During that period, the ratio rose, but that can be partly traced to the increased defense spending that happened. Once again, there’s too many moving parts in the budget and economic growth to give a simple explanation of how the ratio moved.)