Mavericks includes a new feature named App Nap, that pauses applications that are hidden from view, which helps with CPU usage and is supposed to improve battery life on MacBooks.
The App Nap feature has been reported to cause problems with applications that run things in the background, such as rendering video with Premiere and Final Cut Pro. Fortunately Apple has included an option to disable App Nap on an application-by-application basis. Simply do a File->Get Info on the application, and check “Prevent App Nap”. NOTE: This checkbox will not show on applications that have been updated for full Mavericks compatibility, such as Safari and Apple Mail.