I was on the phone with Apple Support again today because Search and Smart Mailboxes in Mail stopped working and they asked me to contact them if this happened again. What was interesting is that once this happens searches in Spotlight would not find anything in Mail. Spotlight searches would find items in the Finder, Messages, and other apps, but nothing from Mail.
Apple Support thinks it may be a problem with Spotlight's indexes.
They had me force Spotlight to rebuild its indexes by going to System Preferences, select SpotLight, and select Spotlight's Privacy tab. They had me drag my hard disk into the box on the Privacy tab to exclude the entire hard disk from being indexed by Spotlight. Then they had me remove my hard disk from the list of locations not to index. According to them, adding and removing my hard disk from that list will force Spotlight to rebuild its indexes for my hard drive.
Apple Support said it may take up to 24 hours to rebuild its indexes for my hard drive, but hopefully this will fix the problem with Search and Smart Mailboxes in Mail. They said to contact them if after 24 hours the problem still occurs.