During Robert’s Rebellion, Mace Tyrell put Storm’s End under siege and maintained the siege until the end of the war. While most fandom focus on the Siege has been on Stannis and the people inside the walls, it’s important to think about Mace and the people outside the walls:

• Mace put Storm’s End under siege rather than pursue Robert Baratheon into the Riverlands, forcing Jon Connington to personally take the field to try to run down the Stormlander army. 
• He kept Storm’s End under siege even when Connington was beaten at the Battle of the Bells and the rebel hosts of the Starks, Tullys, Arryns, and Baratheons united. 
• He kept Storm’s End under siege even after Rhaegar returned and marched to the Trident. 
• He kept Storm’s End under siege even after Rhaegar was defeated at the Trident, and nothing stood between the rebels and King’s Landing. 

Does anyone think that Lord Merryweather, Lord Connington, Lord Chelsted, or the King didn’t send letters in all that time, asking the largest contingent of loyalists in all of Westeros to come to the defense of the king? Pointing out that Mace could easily divide his enormous host and still keep Storm’s End under siege while making a decisive turn in the war by giving the loyalists a numerical advantage over the rebel host? 

Mace stayed at Storm’s End because it was safe, because he is by nature a cautious and conservative man. It’s the same reason that, when Renly was marching on King’s Landing with a massive, seemingly unbeatable host, Mace stayed behind at Highgarden with 10,000 men to keep him safe and stayed there while Randyll Tarly sorted things out at Bitterbridge, and then went to Bitterbridge once things were safe. 

So in a moment of profound uncertainty, with his daughter having been wed to a dead rebel and the Reach politically divided, is Mace Tyrell going to attack Stannis Baratheon on his lonesome, with only the word of Petyr Baelish as surety that he’ll get what he wants after? 

No. Because that’s not what happens. Mace stays at Bitterbridge while Baelish sends riders to get Tywin to force-march down to the Reach and sign onto the deal while there’s still time. And as a result of those riders and Tywin’s speedy arrival, they arrive just in the nick of time.

But any delay, even by an hour or two, means the Battle of Blackwater would have been lost.