It may be possible that the Windows sticky notes in Notezilla are stuck to one or more windows. This is the reason they may show up on desktop.
Can you go back to the stickies that come back from from dead, select one of the sticky note, click on the top left menu and choose 'Stick To Window' option from the menu. Do you see if the sticky note is stuck to any window? You can deselect the windows from the 'Stick To Window' dialog box and press OK. This will disassociate the sticky note with any of the windows.
Watch this video depicting this feature, for more clarity:
Also make sure that the 'Stick To Desktop' option is un-ticked in the note menu.