I primarily use electric power in my PHEV and rarely need to use gas. I am wondering if it’s okay to go several months without refueling, even though the car runs maintenance cycles.
I only use electric too, and my car’s gone months without a gas top-up. As long as you start the engine occasionally, it should be fine. It’s like giving your car a little wake-up call. 
Some PHEVs will tell you when they need to burn a bit of gas. The Volt does this, as does the Prius Prime.