The following are possible reasons (and there are probably more )

the soil is heavy/dense with a large amount of clay in it so the roots are finding it tough to colonise; (solution might be to dig in at least two BIG bucket loads of compost for evey shrub or tree you plant and mix the compost with your natural soil so it's blended. Plant the shrub on a small mound in the hole and fan the roots out so they can spread. A broad hole more than a deep one.

Then add another bucketload the next year and gently stir it through the top inch of soil all around the plant as far out as its branches reach, plus a good layer of mulch. In spring, as soon as you can work the soil safely. ) -

the plants are in a wind alley and the gusts are causing 'wind rock' which snaps or abrades the roots; (possible solution is to stake the plants and also provide some temporary screening/windbreak for at least two years until the roots escape from the ball they formed in the plant-pot or baggie you bought them in. It can take at least that long for some slow growers to move out into new soil.)

The plants are drowning over the winter. If there is a layer of dense clay or even rock below the surface then water cannot drain away and will rise toward the surface leaving the young roots with too much water and no air. (Possible solutions - either dig down to loosen the layer, or drive drain holes through it with a pry bar, or raise the level of the garden. The Rhododendrons won't mind a raised bed at all so long as you provide them with annual feasts of compost and mulch. The Euonymus needs fertile and well-drained soil plus sun so it will go along with a raised bed, too.)

Munchers at ground level - I'm not sure what your local wildlife gets up to, though it does sound more like a soil problem than hungry creatures.