How can I check if something is STILL WITHIN a trigger volume?

This is an alternative solution that may or may not be better for you, based on the situation you are dealing with, but the engine does have shape traces where you sweep through a particular area of space and the trace informs you of whether you have hit a specific type of object within that space. Running this every tick would be much more costly than the “use a variable/array on begin/end overlap” suggestions.

https://docs.unrealengine.com/latest/INT/Gameplay/HowTo/UseRaycasts/Blueprints/index.html#shapetraces