The global data is not persisting. Currently I'm testing it out in a simple loop: I open the game, add 1 to the variable I am testing, save global data, then exit to menu. I start a new game, and the variable has been reset despite it being marked as global data in the plugin.
Viewing post in [CGMZ] Global Data for RPG Maker MZ comments
Could you show your event, and your plugin parameters? Also, could you try turning off all non-CGMZ plugins and seeing if you are still encountering the issue? You can also download and open the demo up in editor from my website, so you can see how the demo accomplished global data.
This plugin does create another save file in your project folder, so it is possible you do not have write access which could cause the creation of this file to fail.