The order seized control of the capital city at the beginning of the Faith Militant uprising, causing the weak King Aenys Targaryen to flee the city, after which he soon died from the stress. He was succeeded by his vicious younger half-brother, Maegor the Cruel, who returned to King's Landing and promptly burned down the sept using the dragon Balerion, while all of the local Faith Militant members were gathered inside for morning prayers.
The sept was never rebuilt. Instead, Maegor ordered the construction of the Dragonpit over its ruins.
In the books
In the A Song of Ice and Fire novels, the "Sept of Remembrance" was so-named in honor of Aenys's mother Rhaenys Targaryen, who had died thirty years before in the First Dornish War - as opposed to Maegor's still-living mother Visenya, who always resented that Rhaenys's son Aenys was put ahead of her son in line of succession. Maegor's destruction of the sept was thus also something of a slight against the rival branch of House Targaryen (though Aenys was dead, Maegor usurped the throne ahead of Aenys's five children three sons and two daughters). A few years later, as if to hammer home his dominance over the Faith Militant, instead of having the sept rebuilt Maegor ordered that a massive "stable for dragons" should be built over its ruins: the Dragonpit.