Hi!
This also happens to me, even with "Check Connection" checked.
It happens when you leave a window open which is left inactive for about half an hour (no one executes any commands in it). To me this mostly happens with SQL Window and Command window, but then again these are the types of windows that I use most often.
If a user wants to close such a window it usually takes about 30s to do so. Meanwhile the PL/SQL Developer is not responding to any commands - if user tries to execute any command, it freezes until the inactive window is closed.
If you have multiple inactive windows open the fastest thing is to log off and back on to the database.
To me it also seems this is more reproducible when you connect to a database over a network (i.e. not to a local database on the computer where PL/SQL Developer is running).
This issue has been around for a long time (at least since v.6 of PL/SQL Developer).
I hope this can help you in tracking the issue. This is actually one thing that bothers me and my coworkers the most in PL/SQL Developer.
Cheers,
Jure