I think a large part of it is due to some sort of quirk in how we read words. In the word "Berenstain", the first two vowels are e's, and I think the brain nat

I think a large part of it is due to some sort of quirk in how we read words. In the word "Berenstain", the first two vowels are e's, and I think the brain naturally expects the next vowel to be an e as well. Also, it's a show/book series aimed at children, and children are much more likely to misread/misspell/misremember things. It'd be interesting to see the demographics of people who remember the "E" spelling vs. those who remember the "A" spelling. It doesn't help that some people, like myself, only ever read the books, and never heard it pronounced on the TV show. And even then, the "ain" pronunciation is still plausible for the "E" spelling (like "vein"). This is all purely theoretical, and I'm no expert, but it seems plausible. I experienced a similar effect when I realised I'd been spelling and pronouncing "Seinfeld" as "Seinfield" for a long time. I was much more willing to accept that I'd been wrong about that though, since, once I started listening a bit closer, I realised there was no way you could pronounce "SeinFIELD" as "SeinFELD".