Are dicarbonyl amides stable in water?
This functional group is an imide. Imides are stable to water and require significantly more effort to hydrolyze than anhydrides (from personal experience). The acyl nitrogen group is a better resonance donor and poorer leaving group than acyl oxygen groups.

From the wikipedia page:


  Being highly polar, imides exhibit good solubility in polar media. The N-H center for imides derived from ammonia is acidic and can participate in hydrogen bonding. Unlike the structurally related acid anhydrides, they resist hydrolysis and some can even be recrystallized from boiling water.


As an example, succinimide, a cyclic imide has a solubility in water of 1 g for every 3 mL - if succinimide reacted with water, such a high solubility would not be possible.

The related N-bromosuccinimide (show below) is also water stable despite that unfriendly looking $\ce{N-Br}$ bond. It is prepared from succinimide in water and an be recrystallized from near-boiling water.