After I plug it back in the compressor refuses to start until it cools off (You can hear the little klixon element clicking on and off inside)
Your system is telling you something.
While the compressor is running it is building up pressure in the high side lines.
When you unplug it, the
high side pressure must be reduced to equal low side pressure before it will start again.
I have found 5 minutes to be ample time.