App Nap is an energy feature introduced to the Mac in OS X Mavericks (10.9) that causes inactive applications to go into a paused state, helping to reduce power usage. The feature can help to prolong battery life for laptops but can cause issues with Connected as it effectively puts the application to sleep and drops the network connection. There, "App Nap" should always be disabled for Connected.
To disable App Nap:
1) Make sure the Connected application is closed.
2) Locate the Connected application in your Applications folder and highlight it with a single click so it is selected.
3) Go to the “File” menu and select “Get Info” (or select the app and hit Command+I)
4) Check the box for “Prevent App Nap”, found under the General section of Get Info screen, as shown in the following screen.
5) Close out of Get Info and relaunch the app in question