1. Keys->New Key, create a key (so you now have a public and private key).
2. Export the public key to some temporary file.
3. Delete the key (public and private).
4. Import the public key from the temporary file.

Refresh. GPA now thinks it has the private key when really it only has the
public key.  Restart GPA and it now knows it only has the public key.

I think I also noticed that when I generated a key in batch mode using the
command line while GPA was open, after hitting refresh, GPA only thought the
key had a public key when in fact there are both.