1. Please download the EM 6.0.2 patch installer from http://www.adobe.com/downloads/updates/ and run it manually to update EM.
2. If it doesn't work, please follow the instructions at http://forums.adobe.com/message/4431136#4431136 to generate log file. The log file name will not be the same as that in the instructions. It would be "Adobe Extension Manager CS6 6.0.2 08-14-2012.log.gz" or similar.