Your best chance to recover your data is to try navigating to the C:\Users<UserName>\AppData\Roaming\Microsoft\Sticky Notes directory, right click on StickyNotes.snt, and select Restore Previous Versions. This will pull the file from your latest restore point, if available.
I've discovered if you close the Sticky Note by right-clicking it on the taskbar, it closes the Sticky Note application. However, next time you open Sticky Notes your data will return. The same also applies if you leave the Sticky Note up when rebooting your computer.
Cheers,
Barbara