Yes. After the ward is reduced to 0HP, it can be brought back using a 1st or greater spell. The key wording is that the ward's "magic remains" after being reduced to 0HP
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
As long as you aren't targeted by Dispel Magic, or some equivalent effect, you will always be able to regenerate your ward. Recreating your ward after a long rest simply ensures that you are topped off every morning.
*Dispel Magic specifically mentions "spells" so it might not drop the ward, but it's worth double checking with your DM.
If the Arcane Ward drops to 0hp, can it no longer regain hp from using abjuration spells?
Example: I have 4/9hp on my arcane ward and cast an abjuration spell of 1st level to bring it up to 6/9hp. I got that.
But if I have 4/9hp and take 4 damage, bringing the ward to 0, if I cast another 1st level abjuration spell, will it or will it not come back at 2hp?
Yes. After the ward is reduced to 0HP, it can be brought back using a 1st or greater spell. The key wording is that the ward's "magic remains" after being reduced to 0HP
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
As long as you aren't targeted by Dispel Magic, or some equivalent effect, you will always be able to regenerate your ward. Recreating your ward after a long rest simply ensures that you are topped off every morning.
*Dispel Magic specifically mentions "spells" so it might not drop the ward, but it's worth double checking with your DM.