I just went through a bunch of my old albums and reglued all the chipboard letters that fell off. I think most of those were self adhesive (peel and stick) and sure didn't last over time.
My go to glue for hard to glue stuff is glossy accents. I've been using it now for some time and haven't had it fail. I use it for all sorts of glossy items.
I think it would also work to use adhesive squares or even a tape roller if the letter is bigger and you could get it on there. I've used mine on metal pieces and larger letters and it does great (permanent ATG).
I would suggest photo squares or glossy accents.
I don't use chipboard often but when I do it's been the self-adhesive ones and I have also noticed them falling off the page so I had to re-adhere them with photo squares.