It's very common for characters to be grounded for absurdly long periods of time even if the mishap they caused was by pure accident, wasn't done out of malice, or even was something beyond their control.
Additionally, any grounded character ("baby show" character or not) can become this if the punishment is disproportionate enough. In this video for example, a girl is suspended from school and grounded by her parents just because she came in last place in a swimming race.
Caillou in Issac Anderson's videos, especially as of late. While Caillou is certainly no saint, the level of cruelty portrayed in the videos makes it hard to laugh at his misfortunes. Boris is shown to be something of a violent psychopath, willing to murder anyone who disagrees with him at the drop of a hat and tortures Caillou at the slightest provocation. Doris, in videos where she isn't absent or dead, helps foster Boris' attitude, turning it into a Never My Fault way of thinking. Even other people are against him - videos have shown his teacher collaborating with Boris to kill Caillou and government officials are willing to turn a blind eye to all of this.
OfficerPoop247's interpretation of Caillou is this for similar reasons to Isaac Anderson's Caillou. Caillou still is a troublesome character, but Officer Poop's videos also have the added caveat that everyone hates Caillou (and other baby show characters), including people who Caillou hasn't even met. Boris is frequently an Ax-Crazy lunatic here, Caillou's "friends" hate his guts, his teacher has been known to laugh at him when he screws up at school, the police have even arrested him just because he's a baby show character (despite him foiling Boris' attempt to rob the bank), and all parties have screwed Caillou over when he did nothing to deserve it. Given how much the world hates him for a rather petty reason, it kinda comes as no surprise that OfficerPoop!Caillou acts out so much.
Dora in the videos by the user adamkleinschmidt2003 comes off as this sometimes as well. Like Caillou, she isn't exactly an angel, but her parents, while not Ax-Crazy like Caillou's parents, sometimes are just downright evil to her, often leading to unfunny situations in some videos, as well. Often they beat Dora up, tell her to her face that they wish she were dead, or deny her basic necessities over incidents that she didn't even cause on purpose or highly regrets afterwards.
Dora is treated even worse in the videos of GoAnimater101Animations2003, where her exploring is done against her parents' wishes and they pretty much wish she was never born, calling her by the cruel name "Dora the Motherfucking Explorer". Other awful names are substituted, and by the time the video ends it's not hard to support Dora running away from home to anywhere else.
Dora in the videos by Alan the Cartoon Maker/Thomas Fan is another big example of this. She still isn't a complete angel, but many videos show her invoking the explosive wrath of her family and friends simply by making honest mistakes or being her normal self. One video even shows Dora's parents getting her arrested for simply even having a show about her. Her parents also hate it when she explores like in GoAnimater101's videos and often refer to her by the derogatory name "Dora the Mexican Explorer", and insult her for being Mexican despite alsobeing Mexican. Even Boots is often against her, and one video shows all of her friends turning against her and beating her up for the simple mistake of forgetting to bring a dish to the picnic. Given that she's probably one of the more innocent versions of Dora in the Grounded videos (and that's saying a lot), one could easily get the desire to get her out of this terrible situation.
Little Bill in several videos. Although he is commonly depicted as having an attitude, all of his family seem to hate his guts, even downright blaming him for minor incidents and things that are caused by the family. In this video, for example, Little Bill is blamed for causing a car crash that hospitalizes a woman, when it was Brenda's fault for turning around and screaming at him. While Little Bill was being a smartass and talking back to his mother, she still took her focus off the road, which ultimately led to the accident. Little Bill even points this out and mentions that it was his mom's actions that caused the crash, but he earns a grounding time of 10,000 years anyway. Another video even has him get his grounding time extended for three weeks (and having to do chores) for simply eating a burger and being caught doing so by Big Bill.
Shaggy, Scooby, Daphne, and Velma in samster5677's videos. They may be idiots, but Fred often punishes them with concussions or death for the most minor things. Of the four, Daphne gets this the most, with this video having Fred kill her by running her over with a lawn mower just because she sold the Mystery Machine to get an iPhone 7.
Specific examples:
Here, Dora sets off a security buzzer at the airport with a large water bottle and gets kicked out of the airport by the security guard. And, of course, she gets grounded by her parents, who, truth to tell, likely bought it for her, let her go through security with it, and brought the ruined vacation upon themselves. And even if they didn't, Dora is only a child and likely didn't see a problem with bringing some water on the flight. Dora is still portrayed as wrong here and everywhere else as she's a "baby show" character, and thus deserves it....somehow.
Caillou couldn't fall under this more than he does in this video, where he foils a bank robbery being pulled by his dad...and not only does Caillou get arrested anyway just because he's a baby show character, he gets the rawest end of the deal even though he didn't even do anything wrong for once. Yet Caillou apparently deserved it and it's a victory for Boris (a Karma Houdini despite being in jail, too) and the police.
Gina Delgado, commonly seen in "Dora Gets Grounded" videos, is treated as this by Dora, simply for being the favored student of Ms. Christina and for having better grades than her. However, most videos show that Gina is actually one of the more neutral characters in these videos, and often does not associate with the troublemakers at all (although she does fall under Not So Above It All every now and then, and is The Chew Toy when it comes to "(Character) Kills (Character)" videos).
Caillou is a big one here, where he drinks some soda that makes him pee so much he floods the world, and is punished by being made to drink it! He did get warned that the soda would make him pee a lot, but he probably had no clue that it would be that bad, and if anything, Boris the Teeth Guy is to blame for selling him the soda knowing it was dangerous.
Justin Bieber is one here where he's meant to be in the wrong for going to school with a cold. While that is inadvisable, since it risks contagion, it's the fault of his parents for sending him there, not of Justin, who didn't even want to go to school in the first place.
for example, a girl is suspended from school and grounded by her parents just because she came in last place in a swimming race.