I've had Continental tires do as you describe. Several, actually. I've had a Panaracer do it too.
700x38c Panaracer Gravelking by
Richard Mozzarella, on Flickr
With Continental, I just gave up & called it wasted money. I sort of figured that between 500 & 5000 miles of use I was unlikely to make much headway in the claims department or be considered to have much in the way of a valid claim no matter how defective they were manufactured.
Under the advice of someone here, at BF, I did let Panaracer know, & they sent me a free tire that was obviously from a different manufacturing lot.
I say contact the company, maybe they'll do right. But they can't have that opportunity if you don't make the first step.