When the coupon inserter, image uploader, expiration date picker, or color pickers stop responding, it is almost always a JavaScript error from another plugin or your theme.
These admin controls all rely on JavaScript loading cleanly on the coupon edit screen. If another plugin or your theme loads a script that errors out, it can stop the rest of the page's scripts from running, which is why several controls break at once.
To confirm and locate the cause, open your browser's developer console, reload the coupon edit page, and look for red error messages. The error usually names the file responsible, so you can tell whether it comes from another plugin, your theme, or Coupon Creator. See Troubleshooting JavaScript Errors for the step-by-step.
If the console does not make the source obvious, narrow it down by deactivating your other plugins and temporarily switching to a default theme, then re-enabling them one at a time. See Troubleshooting Plugin and Theme Conflicts. Once the conflicting plugin or theme is off, the pickers and uploader will work again.