Robert's Rebellion wasn't House Targaryen's fall, the Civil War was

The Targrayens were doing really good as rulers of the 7 Kingdoms despite having continuous conflict with Dorne. No one could oppose them, and the dragons still used to live. A wise man once said, " you are your most powerful enemy." The Targaryens must have not known this, or they may have been able to stay just as powerful and not lose the Iron Throne to Baratheons a hundred and fifty years later.

During the reign of Viserys I Targaryen, there was a dispute between two potential heirs to the Iron Throne: Aegon II and his older half-sister Rhaenyra. 

Rhaenyra was a brave woman and worthy of ruling Westeros. However, Aegon II despite being younger was made the Lord of Seven Kingdoms, and this led to a war- a civil war where brothers fought brothers, dragons fought dragons, nicknamed by the singers as the Dance of Dragons.

Aegon II won the civil war but at a terrible cost. This Civil War was the beginning of the end for House Targaryen as it caused a lot of destruction in terms of wealth, soldiers and their dragons and the Targaryens never truly recovered from this. The resources, power, authority, and trust they lost due to the Civil War were major reasons they couldn't defeat Robert Baratheon. So if you think about it practically, Robert's Rebellion wasn't House Targaryen's fall, the Civil War was.

-----------------------------------------

HBO has planned 6 GoT spin-offs of which the first, House of the Dragon shows this Targaryen Civil War and will be out next year. House of the Dragon follows the story of legendary House Targaryen, their rise and their fall due to the Civil war fought between Rhaenyra and Aegon II Targaryen, two heirs to the Iron Throne.