At the start of Game of Thrones, House Baratheon had taken the Iron Throne from the Mad King, Aerys Targaryen, and it seemed like the house of the stag was poised to become the new ruling family in Westeros for generations to come.
But, for a multitude of reasons, Robert Baratheon became the only Baratheon to ever sit on the Iron Throne. And, by the end of the series the only person even carrying on the Baratheon name is Gendry. But how did the Baratheons lose the Iron Throne almost as quickly as they gained it?
Because They Lacked Political Savvy
Out of the three Baratheon brothers, it seems like Renly was the only one with even a shred of political acumen, and given that he tried to usurp Stannis' rightful place in the line of succession based on his personal popularity, that doesn't say much.
Robert didn't seem to have an interest in politics, Stannis clearly didn't have a mind for politics, and Renly overestimated his political skills so much that he died before he could even get a good shot at the Iron Throne.
Because They Fight First And Ask Questions Later
House Baratheon is pretty well known for its military talents, and that is almost entirely how Robert and House Baratheon won the Iron Throne in the first place.
However, if any of them stopped for a moment and tried to solve their problems diplomatically instead of going to war with their enemies, then they likely could have survived and actually stopped the Lannisters from seizing the throne for themselves. Stannis and Renly fighting each other was one of their worst mistakes.
Because Robert Never Figured Out His Children Weren't Really His
In fairness to Robert, it's not that shocking he didn't suspect that his wife would have an affair with her twin brother, but it is a little odd that he never suspected that she could have had an affair with anyone.
After all, Jon Arryn and Ned Stark both seemed to figure things out relatively quickly, and if Robert had questioned it then he could have replaced Cersei and Jaime's children in the line of succession and avoided a future war.
Because Stannis Listened To Melisandre
Melisandre is certainly a compelling adviser, and Stannis did have legitimate reasons for trusting in what she had to say. However, once his trust turned into unwavering faith, he was pretty much doomed.
Melisandre did truly believe in Stannis right up until his very end, but it's clear that he did many things he didn't agree with and wasn't comfortable with just because she told him to. Melisandre is largely responsible for the end of House Baratheon (or would have been, had Gendry actually been killed).
Because Stannis Killed His Brother
Stannis and Renly clearly didn't agree on much, but despite the fact that Renly was willing to do whatever it took to claim the Iron Throne, Stannis killing him was far too extreme.
Kinslaying is one of the most horrendous sins in the world of Westeros, and while Renly had a significant force, ultimately he had no claim to the throne. Using blood magic to kill Renly would have forever undermined how the rest of the world saw Stannis, even if he became king.
Because Stannis Killed The Last Baratheon Heir
There's a lot of dark irony when it comes to the destruction of House Baratheon, because ultimately after Robert's death, the remaining living trueborn Baratheons simply destroy themselves, their enemies hardly have to do anything at all.
Obviously Gendry solves the issue of having a Baratheon leading the Stormlands, but Stannis had a legitimate claim to the throne, and his daughter Shireen should have inherited after him, so had he not killed her, then House Baratheon may have still won the throne.
Because Renly Wanted Power
While Stannis is largely responsible for most of the horrible things that happen to House Baratheon after Robert's death, Renly isn't exactly absolved of responsibility either. After all, while he and Stannis didn't get along, Stannis simply had the blood right to the Iron Throne.
Renly's quest to take it for himself was a fool's errand, and if he could have swallowed his own arrogance and entitlement then they likely would have won and had the support of all of Westeros behind them.
Because Stannis And Renly Couldn't Unite
There's really guilt on both sides of the war here, as neither Stannis nor Renly could swallow their own pride and team up with each other to defeat their real enemies instead of immediately waging war against each other.
It's an interesting underlying theme of the overall series, families who can't function as a unit wind up destroying themselves and losing their power, and the lack of unity between the three brothers of House Baratheon is a perfect example.
Because Robert Wasn't An Effective Leader
While Robert was undeniably a better king than Aerys, he self-admittedly had no interest in ruling.
And unfortunately, had he actually paid more attention to the people around him or had any political sense at all, he would have seen the problems that would arise for House Baratheon after he was gone and he would have put appropriate plans in place to ensure the stability of his family and of the realm before he died.
Because They Weren't A Family Unit
Tywin Lannister did many things wrong, but one of the few things that he got right was fighting for his family regardless of how he felt about them.
The fact that the Baratheons had no such love between them or weren't even willing to let go of their rivalries in order to work together is largely the reason why Robert Baratheon was the only true stag to ever sit on the Iron Throne.