It could be some cultivars need 100% exposure to be variegated, BUT can
only withstand that in places with chilly summers like Seattle or Northern Europe. So they just don't perform as well in our continental climates (and LI is not as continental as much of the central & eastern CONUS!)

For example I have never seen my 'Dawyck Gold' looking as good as it looks in some pictures from Europe. Some years it is better than others.

Do you plan to eventually plant it out in a sunnier spot?

I'm worried about the same issue affecting my Toona 'Flamingo'. I read somewhere that one reason it never took off as an ornamental in much of the US is the springs are too warm for the pink color to develop consistently. I will find out. Certainly, in the mountains east of Melbourne, AU, they were very spectacular and exotic looking; and if it proves to be a successful plant in my garden, it will be odd that I first saw them there! But that's definitely a maritime climate.

Does your beech show signs of being a grafted clone at the bottom? Otherwise what it looks like is a temporarily variegated seedling that is aging beyond the variegated stage. For instance some other species of trees such as Koelreuteria paniculata, Quercus robur and Styphnolobium (Sophora) japonica produce high percentages of variegated seedlings when raised from seed under nursery conditions. With few of these seedlings remaining variegated after their early years. This is what your tree looks like, as though it is behaving like one of these - making me wonder if the supplier was raising seedlings of the grafted clone and selling ones that happen to come up variegated as duplicates of the original. Of course the likelihood of this depends in part on how apt Fagus sylvatica is to produce variegated seedlings. (And how apt the producer of the material was to send out seedlings under clonal cultivar names, something they hopefully never do).

Otherwise there is an implication that the cultivar you bought is not a good, long proven, stable one. How long has it been around? Maybe somebody had a temporarily variegated seedling come up, named and cloned it without it being old enough yet to see that it wasn't in fact stable. Even many long grown and much circulated variegated shrub and tree cultivars are prone to at least partial reversion - variegation of foliage definitely tends in many instances to be responded to by plant bodies as a malfunction that needs to be gotten rid of.

Thanks. I placed it so it gets afternoon shade as directed by Conifer Kingdom's website. Also another nursery lists this tree as needing afternoon shade to prevent burning. I'll move it to full sun and see if there's any change.

Do you think the scion has been replaced by the rootstock?

Looks to be all the same branches in your two pictures. Also looks like part of the variegated portions have been browning already, so the move to increased sun exposure might not work out.