A lack of irrigation as the potting mix dries out is definitely stressing the plant, but the brown tips were caused by early tender growth this spring that was damaged by an overnight frost/freeze. (Or winterburn, if the shrub produced some new growth last fall, perhaps after a trimming.) Containers dry out must faster than plants in the ground will, and need to be monitored carefully during dry spells and heat waves like this one. Boxwoods have shallow roots compared to most shrubs and have a limited drought tolerance, especially if they are also stressed by growing in full sun. (They're often planted in full sun, but prefer part shade.)

The shrub isn't dying per se -- it actually looks surprisingly unscathed by its site conditions and questionable root system, given the odd angle it seems to be growing at in the corner of the pot -- but the brown tips will need to be trimmed off. They might fall off on their own as they continue to dry out, but it could take a while.

Miri