There are many magic items with charges that replenish at dawn. However, there are places where there is no dawn, like in the Feywild.
I’d think this way of phrasing it was only meant to make sure it restored once per day. But you could argue that since it’s specifically phrased to be at dawn, it doesn’t restore in the Feywild.
Do they actually replenish at some point if there’s no dawn, or will they not replenish at all?