Projected Ward can only absorb one attack 1 per round because it uses your reaction
As you have noted, the projected ward feature states (emphasis mine):
...when a creature that you can see within 30 feet of you takes damage, you can use your reaction to cause your Arcane Ward to absorb that damage.
The rules for reactions state:
When you take a reaction, you can't take another one until the start of your next turn.
So, if a creature takes damage from an attack, and you use the projected ward feature, then you won't have a reaction available to use until the start of your next turn. Thus, if another creature takes damage, you could not absorb that damage using this feature.
However, once you regain your reaction, nothing stops you from using the ward again as long as it has hit points remaining and you meet the range and sight requirements for the feature.
1 I use the term "attack" a bit loosely here. The projected ward can be used any time a creature takes damage, including against effects that aren't attacks; like saving throws against the fireball spell. When I say "attack" here, I'm including any process that deals damage, not just those that are delivered through attack rolls.