One story I remember where the heroine nearly loses her life because she would rather endure what she is going through rather than tell her parents about it. The story is
Witch! from Bunty #1744-1755. When Ellie Ross moves to the village of Littledene she finds the villagers still believe in witches and they think she is descended from the village witch, Elizabeth 'Black Bess' Ross. And it does look like there is a connection, worst luck.

Anyway, the campaign to drive Ellie out of Littledene starts immediately. It gets worse and worse and Ellie has several narrow escapes from being hurt or killed. But Ellie won't tell her parents what is going on because they are enjoying their new life in Littledene. She doesn't even tell them when the villagers smash her mother's pottery workshop.

It is only after Ellie's mother sees her being chased by a lynch mob and calls the police that she finally tells them. They take her away amid more abuse and hatred from the villagers.
Presumably Ellie tells her parents immediately if she has a problem after that experience.
But not all girls were willing to go to such lengths to put up with things. In a similiar story,
Bad Luck Barbara from Mandy #971-986, Barbara Petty is likewise persecuted by the villagers of Wavertree. Unlike Ellie, Barbara keeps trying to tell her parents what is going on, but they just don't get it. Also, Dad is not willing to give up the good job he has in Wavertree. Barbara's misery ends only when Dad receives a transfer to Wales. They move out, with Mum and Dad still oblivious to the villagers' hatred of Barbara.