A/C not turning back on after redline

[Ivary]

My A/C shuts down the compressor at full power to maximize horse power. It is supposed to do that, but then it is supposed to turn back on. Mine does not do that. I have to restart the car to make my A/C compressor turn back on. The dealer charged me $75 to tell me they have no idea, and would I like them to start replacing things until it works correctly. I declined their offer and am relying on the good folks on the forum to have an answer. I am pretty sure it is the controller behind the kick plate on the drivers side, it had been replaced by the previous owner, but I have no idea what wire is the culprit. This has been an issue since I bought the car and I am now motivated to fix it. I would welcome any suggestions.