Wasps can hypothetically sting an unlimited amount of times before they die. Although many species of bee die after a single sting, wasps are able to sting repeatedly with no known end.
The reason that wasps do not die from stinging is that they do not leave their stinger in the flesh after they strike the way bees do. This leaves them free to sting time and again.
While they can insert their stinger multiple times, wasps require time to generate venom, which is what causes much of the pain, itching, swelling and potential allergic reactions to the sting. If a wasp stings multiple times during a short duration, the amount of venom delivered is reduced.