Yes, according to the NIJ, soft armor panels are tested to take six shots of the largest caliber they are designed to defeat. However, depending on the caliber, most bulletproof vests can take a lot more shots, provided the vest isn’t shot at the same exact spot again and again. Some body armor manufacturers stand out from the rest, like Ace Link Armor. Our soft armor panels can take dozens of rounds.
However, you shouldn’t rely on armor that has been damaged to protect you. Once your soft armor vest is shot, it is better to replace it.