I'm new to Java but a few (possibly foolish) ideas occur to me:

1) Make the window modal (using JOptionPane instead of e.g. JFrame).

or
2) Keep track of window state (open, not) in a static boolean tested &
set in the constructor. Though this would need care to eliminate
possible race conditions.

or
3) instantiate the window when the app starts up, thenceforward just use
its setVisible(true) rather than instantiating it. use setVisible(false)
rather than closing it.

I've used option 1 but am interested in finding out what other ways
there are of structuring an application. What approach are you using?