Aye. Each time it actually hits you (or your ally nearby) with a melee attack (besides a reach weapon), it takes the Energy Shield's damage. Generally, you aren't 'stricken' if the creature swings a miss.
This was handy when my halfling copper-dragon shaman and his allies had to go up against a red dragon.....think it was a juvenile red, but it mauled the barbarian and the swordsage and the NPC dragon-slaying ranger (5th level, we hired him cuz the dragon ninja'd the barbarian to death twice previously with death from above) pretty badly with full-attacks. My Acid Energy Shield zapped it with some acid damage though each time one of his natural attacks scored a hit, and that was my only meaningful contribution to its defeat (I went after the kobold cleric that was trying to heal the dragon, with my morningstar; but my aura still helped hasten the dragon's defeat!).