Seriously? Is that like a stargate but for ponies?
Derpygate is a play on the term "Watergate" (the scandal that brought down Nixon).
A minority of the fandom was upset with the fanon name "Derpy Hooves" because they thought it was offensive (some of them thought pretty much everything about Derpy was offensive) and an earlier episode had suggested that her name might be "Ditzy Doo".
Note: Jayson Thiessen said that Ditzy Doo was never her official name, she had a number of names behind the scenes, like Bubbles and Stoneface. When "Derpy Hooves" caught on with the fandom, it also caught on behind the scenes, so Jayson decided to adopt that as her official name.
In the episode "The Last Roundup" written by Amy Keating Rogers, AKR wrote a speaking role for Derpy, and had Rainbow Dash refer to her by name. Tabitha St. Germain provided Derpy's voice, and she sounded a little slow because Tabitha mistakenly thought Derpy was a boy.
About a dozen bronies wrote angry letters to AKR claiming that she was making fun of retards, which really upset her since her own son is retarded. They also wrote to Hasbro and complained.
Then Apple pulled the episode from iTunes. The Hub skipped airing a rerun of it. When the episode finally came back, Hasbro/DHX had straightened Derpy's eyes, redubbed her voice to make it generic, and redubbed Rainbow Dash's lines so she no longer specifies any name.
Hasbro was hit with a flood of angry feedback, but they decided to err on the side that cannot be accused of making fun of retarded people, so the censorship will stand.
There were also hints that Derpy was cut from several of her background appearances post-The Last Roundup.
And that's why Derpy is never going to get her own episode.