Why Does My MBA Close All My Apps After 5 Mins Idle? Sometimes if I walk away from my MBA without locking the screen and I return I'll be faced with a login screen. Once I login all my apps I had open are now closed.

Sometimes I'll close my MBA lid and when I open it again some time later I'll log in and it'll prompt with a bunch of dialogs asking to quit all the apps. I can halt it by hitting cancel.

EDIT Update: The problem has gotten worse. I used to be able to lock my screen Ctrl+Shift+Power/Eject and it'd prevent it from closing all apps. But not even that is doing the trick any longer. I'd try locking then closing the lid and that still does not work.

This is even happening when I'm plugged into a power source.

Output of Console where I believe the MBA killed all apps.  

02/05/15 20:39:10.664 com.apple.usbmuxd[26918]: _SendAttachNotification Device e4:98:d6:19:53:0c@fe80::e698:d6ff:fe19:530c._apple-mobdev2._tcp.local. has already appeared on interface 4. Suppressing duplicate attach notification.
02/05/15 20:39:10.664 com.apple.usbmuxd[26918]: _SendAttachNotification Device e4:98:d6:19:53:0c@fe80::e698:d6ff:fe19:530c._apple-mobdev2._tcp.local. has already appeared on interface 4. Suppressing duplicate attach notification.
02/05/15 20:39:11.416 Xcode[27046]: &lt;DYMobileDevice: 0x7fa25c656030&gt;: failed to acquire service transport reservation: Error Domain=DYAMDErrorDomain Code=-402653150 "The service is invalid."
02/05/15 20:39:27.286 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:27.287 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:27.306 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:27.339 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:27.339 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:27.340 warmd[32]: [_bootcachectl_playlist_for_file:3197] Unable to generate playlist for file: 2 No such file or directory
02/05/15 20:39:48.880 sharingd[26933]: 20:39:48.879 : Starting Handoff advertising
02/05/15 20:39:50.522 locationd[57]: Location icon should now be in state 'Active'
02/05/15 20:39:52.355 locationd[57]: NETWORK: requery, 0, 0, 0, 0, 1, items, fQueryRetries, 0, fLastRetryTimestamp, 444803043.5
02/05/15 20:39:52.926 locationd[57]: Location icon should now be in state 'Inactive'
02/05/15 20:39:52.930 Console[27129]: Failed to connect (_consoleX) outlet from (NSApplication) to (ConsoleX): missing setter or instance variable
02/05/15 20:39:53.462 sharingd[26933]: 20:39:53.462 : Starting Handoff advertising
02/05/15 20:39:55.464 sharingd[26933]: 20:39:55.463 : Stopping Handoff advertising
Looking true your log, I would say it is your Sophos acting up.

SophosUIServer

Uninstall it and live without it. 

It does not do any good anyway AFIK.