From page 115 in the Player's Handbook:
While the ward has 0 hit points, it can't absorb damage, but its magic remains. Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell.
The grouping of the two sentences in that paragraph makes it sound like the intent might be that the ward only regains hit points if it has 0 hit points when the spell is cast.
In a previous paragraph on the same page, it also states:
The ward has a hit point maximum equal to twice your wizard level + your Intelligence modifier.
The maximum would never be reached if the ward only regains hit points when currently at 0 hit points (wizard level will always be greater than spell level). That seems to confirm that we should only consider the second of the sentences above when determining when the ward gains hit points.
Is it correct that Arcane Ward always gains hit points when casting an Abjuration spell of first level or higher, up to the ward's hit point maximum, even if the ward already has some number of hit points?