PL/SQL Developer version: 9.0.0.1601

I'm docking the connections window and on subsequent restart of the program the docking information is lost and connections window becomes a floating window.

How to persist the docking information?

You can either use the Window > Save Layout menu item, or enable the "Autosave desktop" preference (Tools > Preferences > User Interface / Options).

Thank you Marco.

I enabled "Autosave desktop" and docking info is now persistent.

I would like to suggest that by default "Autosave desktop" to be enabled.

If there should be a default autosave desktop, then I suggest to give names for different layouts.
So user is able to store different layout for certain projects, for debug, etc.. and finally have one fix-named "autosave" item, which is automatically restored on startup.