Have you noticed if the cable is hot to the touch or if the radiator hums like it usually does when you turn it on? I'm asking because something that nobody's mentioned is that these devices have an internal thermal safety fuse, and if it trips even once, it doesn't reset on its own. It happens when there's a voltage spike or if the heating element starts to fail. In that case it won't even warm up even if the thermostat works perfectly.
What I'd do is plug it into a different outlet somewhere else in the house, but in a different room to rule out problems with that circuit. Oil radiators use quite a bit of power, and if your wiring has something weird going on or is overloaded, the voltage the device gets might drop. Also check that the cable isn't bent anywhere where you store it or where it's resting, because that degrades the insulation and causes intermittent power cuts.
The thermostat that was mentioned above is a likely suspect, sure, but before assuming it's dead I'd say check carefully where you're plugging the thing in and how you're storing it. After three months it should still be throwing out a lot of heat, so something external to the radiator itself is going on. If it's still the same after you try a different outlet, then it starts to sound like an internal failure.