After crash, apps still appear in dock but no active process and cannot force quit.

I'm running an iMac 5K newly updated to El Capitan. Since the update, I've had an extremely frustrating problem occur a few times, earlier with Chrome and most recently with the Mail app. While I'm working with the app in the forground, something happens causing the app to freeze and then "quit." However, after the app "quits" the icon in the dock is still showing an active app. Clicking on the icon in the dock does nothing. Right clicking on the icon yields the "Application not responding" message. Force quitting the app either through right clicking on the dock icon or through the force quit menu has no effect. When I look in Activity Monitor, there are no related processes to kill via terminal either. Trying to restart the computer doesn't work either because I get a warning telling me that the app in question will not quit and is preventing a restart. The only way I have been able to fix this is with a hard restart at which time the app seems to be functioning perfectly.

Any ideas?

Peace-

Erik