Downward flame spread over thin electrical wires is investigated at reduced gravity. The wire is made of a Nickel/Chrome (NiCr) core coated with Low Density PolyEthylene (LDPE). The flame spreads in an opposed flow and the conditions of the free stream, i.e. oxygen content, pressure, and forced flow velocity, are varied. Parabolic flights allow experiments to be performed at various gravity levels to reproduce conditions met on Earth, Mars, the Moon, or in microgravity. Past studies showed that dripping of the molten coating occurs at Earth gravity but disappears in microgravity. A new process is here systematically observed at intermediate gravity levels: while the flame front spreads at a steady rate, a molten droplet of the LDPE coating exhibits a cyclic motion ahead of the flame front. This is driven by the balance among the gravitational, viscous, and adhesion forces. Gravity primarily powers the force driving the droplet away from the flame front, while the adhesion force ensures the droplet’s attachment to the wire. The viscous force critically influences the droplet’s velocity, which shows an inverse relationship with viscosity. This specific cycle can be decomposed into two stages where the aforementioned balance can be evaluated to clarify the conditions of the cycle’s existence. Experimental results show that increasing the oxygen content tends to shorten the cycle by increasing the velocity of the flame front, while increasing the pressure also shortens the cycle by increasing the cooling rate of the droplet. This cyclic behavior can trigger flame extinction at Martian gravity levels, even in scenarios where flames propagate under normal and microgravity conditions. These findings can significantly impact fire safety strategies in environments with intermediate gravity levels.