Only appears to be a single version running.
I tried replacing with a fresh copy from alfredapp.com, but the issue persisted.
Repairing disk permissions did not help either.
After all these attempts failed, I tried copying the preferences file from my Dropbox/Backups folder to the desktop and switched Alfred's sync preferences to that file. Upon restarting, my appearance settings and custom searches had all returned!
Next, I tried copying the preferences file to another location in Dropbox (Dropbox/Alfred). Setting the sync folder to the new location worked as well.
Finally, I deleted the original preferences file and replaced it with the copy from Dropbox/Alfred and returned Alfred's sync setting to Dropbox/Backups. Everything is working great again.