One troubleshooting step that will help narrow down what’s causing the promotion code to not apply is use the WordPress Health Check plugin to rule out a plugin conflict. Here’s how to do that:
You install the Health Check plugin, then go to WP → Dashboard → Heath Check → Troubleshooting. There you’ll Enable Troubleshooting Mode, then once that’s activated you’ll reactivate Event Espresso and the Promotions add-on only via the Health Check’s Troubleshooting item in the WP admin bar. At that point, can you check to see if the issue persists?