Cersei in A Song of Ice and Fire. In book 1 she successfully engineers her husband's death and beats out Ned Stark in the power struggle that follows, and while she's ultimately bested by the Imp in book 2, she's not a pushover. In book 4, though, she surrounds herself with morons and alienates everybody useful as if she's doing it on purpose - Littlefinger aptly describes her as "stumbl[ing] from one idiocy to the next." One interpretation is that she's gotten stupid and arrogant from her success, which matches this trope. But it's also possible that she's no dumber than before, and has simply been promoted to the level of her incompetence, Peter Principle-style. The Seven Kingdoms are not an easy realm to run.
Another interpretation is that while she started out reasonably smart, the events of the end of the third book ( her son Joffery's murder, her brother Tyrion's escape before he can be executed for said murder, and her twin Jamie's reluctance to continue their incestuous affair) has unhinged her. It helps that everyone capable of overriding her bad decisions is dead or has left King's Landing by the fourth book. Alternately, she was never that smart in the first place: she beats Ned more through Ned's insistence on Honor Before Reason than her own cleverness, helped along by people like Littlefinger because she was a useful and predictable tool for conspirators who were already planning the next dynasty (or two) to succeed her. Until the readers start getting chapters from her perspective, she seems relatively competent (if petty and occasionally outmatched) in her scheming and politicking.
A more prosaic explanation is that she has been steadily increasing her alcohol consumption over the course of the story, which is noted by several characters. By the time things really start falling apart in book 4 she drinks as much or more as her late husband did, while sharing his disdain for actual ruling. She also lacks his self-awareness of the problem or the support structure he relied on to compensate for it.
Claudia from The Babysitters Club started out as a C-student who had an above average I.Q. but just didn't care about doing well in school. By the end of the series, she was so dumb the reader sometimes wondered how she managed to put on her pants in the morning.
Kalten in The Elenium seems to get a case of this. In the beginning of the trilogy, he is a skilled knight although he is incapable of performing magic because he couldn't pronounce the Styric language. By the end of the second book, this has turned into him not knowing what a diagonal is. Subverted at the end of the Tamuli where he reveals that he is playing the Obfuscating Stupidity card, since he knows that if people don't take him seriously they will be off-guard around him.
Septimus Heap in Septimus Heap, between Syren and Darke. In Syren he the cautious one, in Darke his disregard for Jenna's warnings about the Darke Domaine doesn't match any of his past actions, and results in the Domaine being set loose.
Sherlock Holmes: Watson is compentent in the originals novel, though his mediocrity does serve to highlight the main character's brilliance. In many adaptations he has taken a level in dumbass: few of which have portrayed him with any of his original intelligence or abilities.
The Wheel of Time: In the first four books of the series Elaida is presented as a cunning member of the Red Ajah who is able to get Suian removed from power and still her. As soon as she gain powers her I.Q drops considerably, she pisses everyone in the tower off, she makes disastrous decisions that causes Aes Sedai to be captured, and she can't even decide that the Black Ajah exists or not even when it should be obvious after several sisters were murdered and Ter'angreal were stolen. The reason for the change is that she was briefly visited by Padan Fain, whose powers include the ability to corrupt people and drive them insane. His influence was only a 'brush' of his normal power, but it was enough to start a slow deterioration.