Microsoft has been giving a lot more attention to its Windows 10 Sticky Notes app of late. The app's recent 3.0 release was headlined by cross-device sync support, powered by Outlook. Unfortunately, you still can't recover deleted notes from within the app – but the Outlook sync feature means all is not lost if you accidentally remove something important.
When you delete a note using the Windows 10 app, you're asked to confirm the deletion before the note vanishes from the list. There's no indication that you can recover the note later, but neither there is a warning that it will be gone forever. The online experience – part of OneNote Online – does ask whether you want to "permanently delete" the note, but this isn't actually what happens.
Since all Sticky Notes are now synchronised to your Microsoft account, via your Outlook email, you'll find every deleted note ends up in Outlook's "Deleted Items" folder. To recover a note, just open Outlook – the web version, Windows 10 Mail app, or Outlook 2016 desktop client – and head to Deleted Items.
Look for the "Restore" button in whichever client you're using. On the web, select the item and press the "Restore" button on the top menu bar. Within Outlook 2016, you may need to use the "Move" option to manually move the note back into your "Notes" folder. Once it's restored, it should automatically reappear in the Sticky Notes app after a few moments.