It happened in the very first episode of the very first season. Nightmare Moon popped up, carried out her plan, removed her sister, set her traps, destroyed the Elements of Harmony...except that last step turned out to have failed.
Happens in "The Return Of Harmony". Discord has emotionally broken and Mind Raped five of the Mane Cast already to the point the Elements Of Harmony — the only magic that can defeat him — are useless and driven Twilight Sparkle across the Despair Event Horizon, completely shattering the mane cast's friendship. With the heroes crushed and beaten, Discord takes over Equestria, transforming it into a surreal World Gone Mad that's growing more chaotic by the moment, with Ponyville as his new "chaos capital of the world". However, his victory is snatched away from his grasp when Celestia sends Twilight all the letters her student had sent her over the last season, which restores Twilight's hope and motivates her to restore her friends to normal. Reunited, the group confront Discord and his own pride and belief the Elements of Harmony won't work causes him not to realize this until its too late. Discord is sealed away and a World-Healing Wave created by the Elements of Harmony restores Equestria to normal.
Happens again in the Season 2 finale. The Changeling Queen has destroyed the barrier protecting Canterlot, unleashed her hordes upon the city to feed off the love of all the ponies, and has even defeated Celestia in a straight-up fight by tapping into Shining Armor's love for Cadence. Even worse, the Mane 6 fail to reach the Elements of Harmony in time, and are captured by the thousands of changelings that now storm the city. Unfortunately for the queen, she forgot that Cadence and Shining Armor are still in the room, and that Cadence's magic is the ability to make ponies love each other. The result is Shining Armor getting a massive injection of the Power of Love, which gives him enough power to reset the barrier and blast all of the changelings out of Canterlot once and for all.
The Season 3 two parter also has this happen, with a twist. King Sombra's near victory is the result of his actions taken before the story even starts. Cadence's magic gives out, causing the barrier keeping Sombra locked out to fail and Sombra himself to enter the Crystal Empire. Twilight ends up trapped by a crystal barrier, which also begins to corrupt the Empire from the inside and prevents her from getting the Crystal Heart where it needs to be defeat Sombra. Spike manages to get the Crystal Heart and try to get it to where it can defeat Sombra, but Sombra attacks, coming within a few inches of capturing or possibly killing him before Shining Armor throws Cadence like a javelin to catch Spike and the Heart, allowing them to power it up and kill King Sombra.
"Twilight's Kingdom, Part 2", Tirek claiming Discord's magic and all the magic Twilight had been carrying with her means he had technically won. There wasn't a creature alive in Equestria with enough magic to constrain him at that point. So the team has to tap into an 11th-Hour Superpower to break through.
Twice in the made-for-TV movie, My Little Pony: Equestria Girls – Rainbow Rocks. First, the Hu-Mane Six are sent down a trapdoor and Locked in a Room under the stage, and the negative energy produced by their argument begins to give the Dazzlings more power than they dreamed of, but Sunset Shimmer snaps them out of it and Spike fetches DJ PON-3 to unlock the door. Second, during the final battle, the Dazzlings' siren avatars initially overpower the Rainbooms, knocking the mic from Twilight's hands, but Sunset grabs it and joins the band along with DJ PON-3 providing a beat, allowing them to summon their own alicorn avatar and turn the tide.
In "The Cutie Map", Starlight Glimmer is only defeated thanks to three chance reasons: The ponies get lucky and expose her fake cutie mark, the townsponies (who willingly followed her philosophy to begin with) decided to turn on her rather than accept her well-justified reason for keeping her own cutie mark, and those random villagers managed to (just barely) stop Starlight before she escaped. This is probably the closest the main cast ever came to utter defeat, and that is saying a lot.
It's only made worse in the Season 6 finale, "To Where and Back Again", as within the span of a few hours that Starlight Glimmer was out of Ponyville visiting her old village with Trixie, Queen Chrysalis and her Changelings, in both another invasion attempt on Equestria and Revenge on the Royal Family and Elements of Harmony for her previous defeat at the Royal Wedding, have managed to sweep into the country and kidnap all of them without being discovered, replacing all of them with fakes. Every Alicorn Princess, Shining Armor, Spike, and the Mane Six, have been taken back to Chrysalis' hive to be kept prisoner in cocoons, with their magic inaccessible due to Chrysalis' throne, leaving it up to Starlight, Trixie, Discord, and Thorax to mount a rescue attempt that ultimately fails. That is, until Starlight convinces Thorax to willingly give Chrysalis his love energy, sending her flying into her throne and cracking it. This causes Chrysalis' own Swarm to turn on her, and the resulting surge of love energy ends up destroying her throne and throne room, frees her prisoners from their cocoons as the throne room's destruction caused the cocoons to fall and break open, and with her sorely outnumbered by the Royal Family, Elements of Harmony, Master of Chaos, her reformed Swarm, and their new leader, King Thorax, Chrysalis has no choice but to retreat in utter defeat, but not without swearing a new vendetta against Starlight for taking everything away from her.
In My Little Pony: The Movie (2017), the Storm King managed to gain the power he wanted and nearly destroyed all of Equestria with his created storm. He only lost due to the Mane Five ramming into him with Pinkie's giant cannon (which was a lucky shot) and Tempest's Mistreatment-Induced Betrayal later on.
In the climax of the Season 8 finale "School Raze", Cozy Glow has manipulated the students into turning against Chancellor Neighsay and the non-Pony creatures, and is destroying all magic in Equestria. She comes within two seconds of sending the Young Six to another dimension, but the Tree of Harmony saves them, and they foil her plan and restore the magic.
In the Grand Finale "The Ending of the End", Tirek, Chrysalis, and Cozy Glow have stolen the magic of Celestia, Luna, and Discord, destroyed Canterlot Castle, captured Twilight's friends, caused the pony tribes to turn against each other to the point that it draws back the Windigos, and sent Twilight close to the Despair Event Horizon. It's only through a Rousing Speech by her friends and the cavalry consisting of every creature introduced in the series that Twilight is able to stop the villainous trio.
