So here is my current understanding of the cause of this and a solution that is little bit better than what has been proposed here by others.
There is are two system processes
/usr/libexec/pboard
/System/Library/CoreServices/pbs
Looks like these processes are responsible for holding and maintaining the paste buffer ( OS X name for the clipboard). These processes also maintain a system socket that other application talk to, that's how they can exchange the cut and paste material
There was a change introduced in the past few month that causes this processes to to fail and quit sometimes. They may or may not get automatically restarted by the OS X. But even when they do get restarted,
But even after the process is restarted the other applications are still trying to talk to the old socket. For which nobody is listening to.
So my solution is to check if these processing are running, if not restart them. And then restart the applications for which the Cut and Paste is broken.
This is not ideal solution, it's pain to restart Google Chrome and PyCharm with dozens of tabs and windows open, but that's bit better than restarting everything