1. Click on "Minify" menu item on the left side (probably under "Performance")
2. Find "Never minify the following JS files" text area
http://YOUR-DOMAIN-NAME/wp-content/plugins/comprehensive-google-map-plugin/assets/js/cgmp.framework.min.js. You can obtain the link by inspecting the HTML source of your page where the map is, when W3 Total Cache is DISABLED (otherwise you would not find it since W3 Total Cache would cache it).
Please make sure that the JS link is valid(!) before adding in the text area: paste it in the browser's address bar and try to load it. Do not guess.
Don't worry about decreasing performance of your page by thinking that you are increasing the page load time - the plugin's JS is ALREADY minified using Google's Closure Compiler. In other words, there is no point letting W3 Total Cache to minify ALREADY minified JS file. When the latter happens, the Google map plugin stops working.
4. Clear all cache