I could not reproduce but I can think of 2 possibilities...

1) From examining the code, I can see that during page loading it would not close tooltips. This is now fixed.

2) Some of the tooltips are click to open/close. These are ones that typically exist on help buttons, and are like this so that tablets/mobiles can use them.

The tooltip mechanism should be very robust, but if you still find issues please report in some more detail. E.g. if you hover over something else with a tooltip, does it close the tooltip you had open? What exactly would you do to reproduce, just normal stuff, or tab switching, or frantic mouse movement, or keypresses?

I did just notice and fix an issue on the "choose which template to edit" screen. It was a very specific problem on that screen though.