Ok, first to briefly explain your power steering system. It is a bit of a hybrid system in that it incorporates both the traditional hydraulics with power steering fluid and lines, with the electronic power steering with a hydraulic power steering control module that is coupled to a fluid pump.
Because turning the engine on and off and back on restored the power steering for a bit, this points to a problem in the electronic portion. If it were hydraulic(fluid) issue, turning the engine off and back on would not affect it. The warning light being on further points to this as it only sets when a fault in the electronics is detected by the onboard computer.
This may be an intermittent short in the wiring harness at the control module due to chafing that has allowed fluid intrusion, or may be an internal fault in the electro hydraulic control module located at the pump(see attached)
You can check the wiring for any cuts, chafing or breaks and repair as needed. IF ok, then most likely the control module, which would need to be replaced and new one programmed with factory level scan tool and software. The control module is part of the pump assembly and replaced as a unit, which lists for $776
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