Benny Kjær Nielsen, developer of MailMate, describes the problem:

Since Apple released the 10.8.2 update for Mountain Lion I have received several reports about MailMate being slow and unable to detect spam. The problem turns out to be that the AppleScript communication between MailMate and SpamSieve breaks down. Each request sent by MailMate to SpamSieve hangs for 2 minutes before failing with a timeout error. This happens for every incoming message.
He’s built a new version of MailMate that works around the problem. GyazMail is also affected, and the developer is working on a new version.

The same OS bug affects Postbox, and I’m working with the developers there to get their SpamSieve plug-in updated with the workaround. As a temporary workaround, you can enter the following command in Terminal:

sudo killall -KILL appleeventsd
This will restart the appleeventsd process, which should allow the applications to communicate again.