This posting is older than 6 months and can contain outdated information.
Regarding App Nap:
OS X Mavericks introduces a new feature called "App Nap" that puts applications to sleep that the systems thinks you are not using. It does so for all applications, regardless of when they were released.
As a background application without a window that you regularly interact with with your mouse or keyboard, Remote Buddy can be considered "inactive" by OS X Mavericks and put to "sleep", which will give you all kinds of weird effects.
The upcoming update of Remote Buddy will tell OS X Mavericks not to put it to "sleep" by itself. If you're using an earlier release, however, you'll need to tell OS X Mavericks yourself that you don't want "App Nap" for Remote Buddy. Doing so is pretty easy:
1) Select Remote Buddy in a Finder window
2) Press Cmd + I (or right click its icon in a Finder window and select "Get Info")
3) Use the available checkbox in that window to disable App Nap for Remote Buddy
4) Relaunch Remote Buddy
Hope that helps.
Best regards,
Felix Schwarz