MacBook Air (10.11.6) will not restart or shutdown on its own

I've had this problem for about a year where my MacBook will not restart or shutdown on its own. If I click restart or shut down, even when associated with an update, it will begin to shutdown and clear all open applications and icons on my desktop but stop and pause indefinitely on my now-empty desktop. To shutdown or reset, I have to press and hold the power button. It reboots but the update never takes effect. Does anyone have any suggestions to fix this problem? Thanks!