Update: The document originally recommended disabling Bluetooth, but it appears updating to the latest version of OS X is Apple’s recommended fix. Much better.
In a support document issued today, Apple addressed a known issue with AirPlay Mirroring performance freezing or dropping out. MacBook Pro and Mac Pro users with last year’s models may see the issue when using an 802.11 b/g network…
Apple’s solution? Disable Bluetooth. For Mac Pro users, that means breaking out the wired mouse and keyboard as it has no integrated input and turning off Bluetooth means disconnecting the signal from a Magic Mouse and Apple Wireless Keyboard.
Since the issue seems to be constrained to 802.11 b/g networks, upgrading your network base station might be a better solution.