I am with @tmcgahey on this one. I have helped 2 neighbors setup their Rachio in the last month and zero issues.
Do you have another receptacle near the Rachio that you can try? Preferably on another circuit breaker. Run an extension cord from it to power your Rachio and see if it exhibits the same behavior. You could even disconnect the Rachio from irrigation wires and wall and power it inside your home to see if it power cycles there an an experiment too. If it doesn’t then something is up with the receptacle/circuit that you are currently plugging your Rachio into.