The most common reasons of this error are listed below.
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Errors may be highlighted in red. If you see any errors in console you should eliminate them for correct operation of plugin. Please read this codex article carefully.
Numerous themes and plugins were created for WordPress. Unfortunately, not all of them were written according to standards and code of WordPress. Incorrectly written themes and plugins often prevent correct operation of other plugins and themes.
Open the page with inactive “Insert shortcode” button. Open Dashboard – Plugins page in a separate browser window (or in a new tab). Disable all active plugins except of Shortcodes Ultimate. Then enable plugins one by one. Refresh the page with “Insert shortcode” button after every activated plugin. In such a way, you can easily find faulty plugin.
Try to change your active theme for one of standard WordPress themes, e.g. Twenty Fifteen or Twenty Sixteen. If “Insert shortcode” starts to operate correctly, then your theme is most likely incompatible with Shortcodes Ultimate plugin.