Hello,
Sorry to hear you are having issues. First, make sure your Groupy is enable.

Second, please review your Grouping Setting: Manual Grouping by drag and drop Try changing those setting. I usually set mine to "Only group windows when the ctrl key is held down". Also do know, make sure you're click and drag on the titlebar not on the tab. Some application like browser have tabs, you can click and drag on a tab to move that tab away from that browser. But you can not drag that tab into another windows to group it by Groupy. You will need to click and drag on the titlebar for that.

Try that if that still do not work. You might need to check your Groupy rules section.
Thank you.
Basj,
Stardock Community Assistant.