If I open my extension popup then I open another window or tab following the popup does not stay open if I return to it.
Is there a way to force it so the popup stay
If you enable panels at "chrome://flags/#enable-panels" you can use something like:
chrome.windows.create({ url:"popup.html", type:"panel", width:300, height:200 });
to open a panel window instead which will stay on top all the time as long as you don't move it from the bottom of the screen.