I recently upgraded my late 2011 generation iMac to OS X Mavericks and began to note the various differences, some good some bad. One bad one was how App Nap effected Microsoft Outlook, it was driving me crazy!
When I was not at my computer, or working on a different desktop than the one I dedicate to outlook, I wasn't getting messages pushed through!! After a bit of searching I found out about Mavericks new "App Nap" feature. While I like this for some applications, such as a Photoshop or Final Cut Pro, it does not work for applications you want to continue to work in the background, like Outlook.
I found the fix...
Begin by finding the App you want to disable in your Applications Folder, then right-click and select Get Info from the drop down menu. Then you can check the "Prevent App Nap" as shown above. You must then close and reopen the application for this to take effect! App Nap will not be disabled until you have rebooted the app.