Mac Screen Goes to Sleep Mode Even When Set to Never Sleep

Check the date for the file: com.apple.screensaver.50A10F0D-581E-5D09-8966-646EE8532C5B.plist in Libary

after you made the time change, it should show the latest date/time.

If not, delete the file.

You can get a list of power assertions by running pmset -g assertions:

$ pmset -g assertions
10/27/13, 8:48:55 AM GMT
Assertion status system-wide:
   BackgroundTask                 1
   PreventDiskIdle                0
   ApplePushServiceTask           0
   UserIsActive                   0
   PreventUserIdleDisplaySleep    0
   InteractivePushServiceTask     0
   PreventSystemSleep             0
   ExternalMedia                  1
   InternalPreventDisplaySleep    1
   PreventUserIdleSystemSleep     1
   NetworkClientActive            0
Listed by owning process:
   pid 189(coreaudiod): [0x0000000100000617] 00:00:19 NoIdleSleepAssertion named: "com.apple.audio.'AppleHDAEngineOutput:1B,0,1,2:0'.noidlesleep"
   pid 9879(backupd): [0x00000001000005f1] 00:13:17 PreventUserIdleSystemSleep named: "Time Machine backup"
   pid 9879(backupd): [0x0000000c000005f0] 00:13:17 BackgroundTask named: "Time Machine backup"
   pid 18(powerd): [0x00000009000005e1] 00:13:47 ExternalMedia named: "com.apple.powermanagement.externalmediamounted"
   pid 18(powerd): [0x00000011000002e1] 00:00:00 InternalPreventDisplaySleep named: "com.apple.powermanagement.delayDisplayOff"
    Timeout will fire in 299 secs Action=TimeoutActionTurnOff
Kernel Assertions: 0x4=USB
   id=500  level=255 0x4=USB mod=10/26/13, 6:38 PM description=XHC1 owner=AppleUSBXHCI
   id=501  level=255 0x4=USB mod=10/26/13, 6:45 PM description=EHC2 owner=AppleUSBEHCI
   id=502  level=255 0x4=USB mod=10/27/13, 8:48 AM description=EHC1 owner=AppleUSBEHCI

In the output above, Time Machine is preventing idle sleep.